user8157: In SN 24.5, the Lord Buddha criticized the following doctrine called "natthikavādaṃ": 

There is no benefit in giving, sacrifice or offerings. There’s no fruit or result of good and bad deeds. There is not this world or the
  other world. There are no duties to mother and father. No beings are
  reborn spontaneously. And there’s no ascetic or brahmin who is well
  attained and practiced, and who describes this world and the other
  world after realizing it with their own insight.
This person is made up of the four primary elements. When they die, the earth in their body merges and coalesces with the main mass of
  earth. The water in their body merges and coalesces with the main mass
  of water. The fire in their body merges and coalesces with the main
  mass of fire. The air in their body merges and coalesces with the main
  mass of air.
The faculties are transferred to space. Four men with a bier carry away the corpse. Their footprints show the way to the cemetery. The
  bones become bleached. Offerings dedicated to the gods end in ashes.
  Giving is a doctrine of morons. When anyone affirms a positive
  teaching (atthikavādaṃ) it’s just baseless, false nonsense. Both the
  foolish and the astute are annihilated and destroyed when their body
  breaks up and don’t exist after death.

According to SN 24.5, why did the Lord Buddha criticize natthikavādaṃ (the doctrine of disbelief)? 

user471: There is a related sutta, SN44.6 that says:

"For one who loves form (and the rest of the five aggregates), who is
  fond of form, who cherishes form, who does not know or see, as it
  actually is present, the cessation of form, there occurs the thought,
  'The Tathagata exists after death' or 'The Tathagata does not exist
  after death' or 'The Tathagata both exists and does not exist after
  death' or 'The Tathagata neither exists nor does not exist after
  death.'
"But for one who doesn't love form (and the rest of the five
  aggregates), who isn't fond of form, who doesn't cherish form, who
  knows & sees, as it actually is present, the cessation of form, the
  thought, 'The Tathagata exists after death' or 'The Tathagata does not
  exist after death' or 'The Tathagata both exists and does not exist
  after death' or 'The Tathagata neither exists nor does not exist after
  death' doesn't occur.
"For one who loves becoming, who is fond of
  becoming, ...
"But for one who doesn't love becoming, who isn't fond of becoming ...
"For one who loves clinging/sustenance ...
"But for one who doesn't love clinging/sustenance ...
"For one who loves craving ...
"But for one who doesn't love craving ...

I have heard another story about a master saying "think about monkeys", and the meditator thinks about monkeys with his eyes closed. After this, the master says "don't think about monkeys", and again, the meditator never fails to think about monkeys with his eyes closed. Why? Because in both cases, he has an obsession with monkeys.
Similarly, views about whether 'The Tathagata exists after death' or 'The Tathagata does not exist after death' or 'The Tathagata both exists and does not exist after death' or 'The Tathagata neither exists nor does not exist after death' all occur only if one has an obsession with the five aggregates, becoming, craving and clinging.
Similarly, having views about whether one (the self) 'exists after death' or 'does not exist after death' or 'both exists and does not exist after death' or 'neither exists nor does not exist after death' are all due to obsession with the five aggregates, becoming, craving and clinging.
The Acela Sutta shows that the Buddha teaches the Right View using dependent origination, rather than eternalism or annihilationism. (This comes from here but the full text can be found here):

Again, when the Buddha was asked by the naked ascetic Kassapa whether
  suffering was of one's own making or of another's or both or neither,
  the Buddha replied "Do not put it like that." When asked whether there
  was no suffering or whether the Buddha neither knew nor saw it, the
  Buddha replied that there was, and that he both knew and saw it. He
  then said "Kassapa, if one asserts that 'He who makes (it) feels (it):
  being one existent from the beginning, his suffering is of his own
  making,' then one arrives at eternalism. But if one asserts that one
  makes (it), another feels (it); being one existent crushed out by
  feeling, his suffering is of another's making,' then one arrives at
  annihilationism. Instead of resorting to either extreme a Tathaagata
  teaches the Dhamma by the middle way (by dependent origination)"
  (S. XII, 17/vol. ii, 20).

The Yamaka Sutta also speaks of an interesting notion:

"Then, friend Yamaka, how would you answer if you are thus asked: A
  monk, a worthy one, with no more mental effluents: what is he on the
  break-up of the body, after death?"
"Thus asked, I would answer, 'Form is inconstant... Feeling...
  Perception... Fabrications... Consciousness is inconstant. That which
  is inconstant is stressful. That which is stressful has ceased and
  gone to its end."
"Very good, my friend Yamaka. Very good.

So, rather than saying that after Parinibbana, the Buddha exists or does not exist, it's better to say suffering has ceased and gone to its end.
In a similar way, rather than saying that after death, whether an unenlightened person is non-existent or existent or reborn or not reborn, it's better to say that suffering has not ceased. And what happens when suffering has not ceased, is understood using dependent origination.

user43: Why did the Buddha criticize natthika (moral nihilism)?
Well, it is wrong on many levels:

objectively, moral nihilism leads to careless behavior, which often leads to conflict and suffering.
subjectively, adhering to good morals is a nice rule of thumb for reducing mental afflictions - while moral nihilism would give free reign to the blinding passions.
Right Dharma by its very nature has to be based on reality of how things work - and being based on how things work means its principles can be observed throughout a wide range of human activities - which is why worldly ethics and Buddhism go along 90% of the way. Moral nihilism goes contrary to worldly ethics, which means it's not in accord with how things work.
the entire Buddhist path is based on the idea that some states of existence are "better" (more peaceful) then others, Nirvana being "the best", with better behavior leading to better states, and better views leading to better behavior. Dharma is that "better view". To claim that moral nihilism is the right teaching would imply that moral nihilism is a better view, which is logically inconsistent, since from the standpoint of moral nihilism there cannot be such thing as "better view".
our ideas and results of our actions continue to exist after our death. So whatever we do has influence beyond this life, just like we have inherited actions of previous generations. Moral nihilism denies this factor, this denial being obviously false. 

How is this reconciled with the highest (Mahayana's) teaching of emptiness? Emptiness, or groundlessness as it is sometimes called, does NOT mean there is no good & bad. It does NOT mean there's no skillful & unskillful behavior. It means good/bad and skillful/unskillful cannot be simply generalized and reified. This is known even from the modern ethics with its infamous trolley problem. Good & bad is not something you can decide once-and-for-all and always go by the same rule. Same goes for skillful/unskillful. If being wise and skillful were as simple as learning a rule of thumb, everyone would be a buddha by now.
It also involves clear understanding that, in any kind of dispute, to be too attached to one position as "the only good" - is not good, because it leads to trouble. Attachment to reified morals, aversion based on that attachment, and conflict it generates - is not the most skillful approach. It is better than having no clue, sure - but not as good as seeing the situation from all perspectives at once.
So from Mahayana perspective, moral categories are not tangible, they cannot be grasped. Morals and wisdom is a skill one has to master, and the more someone masters it, the more nuanced and less stereotyped it gets, until it's almost like it has no definite shape - and yet you can see it working with clarity.
At the very end of this progression of mastery is what Mahayana calls groundlessness or positionlessness of a great master. Nothing can be further away from the moral nihilism.

user11541: The answer is present in the same sutta:

“When form exists, because of grasping form and insisting on form, the
  view arises: ‘There’s no meaning in giving, sacrifice, or offerings. …
  Both the foolish and the astute are annihilated and destroyed when
  their body breaks up, and don’t exist after death.’ When feeling …
  perception … choices … consciousness exists, because of grasping
  consciousness and insisting on consciousness, the view arises:
  ‘There’s no meaning in giving, sacrifice, or offerings. … Both the
  foolish and the astute are annihilated and destroyed when their body
  breaks up, and don’t exist after death.’

In other words when self identification with forms,feelings,perception,consciousness and/or volitional formations occur such a view as highlighted by you also occurs.
I think the the wrong view of moral nihilism gets generated when we say that every self ceases to exist after death(i.e body and self are same) or that every self lives for eternity(i.e body and self are different). In both the case following holds true :

‘There’s no meaning in giving, sacrifice, or offerings. There’s no
  fruit or result of good and bad deeds. There’s no afterlife. There are
  no duties to mother and father. No beings are reborn spontaneously.
  And there’s no ascetic or brahmin who is well attained and practiced,
  and who describes the afterlife after realizing it with their own
  insight. This person is made up of the four primary elements. When
  they die, the earth in their body merges and coalesces with the main
  mass of earth. The water in their body merges and coalesces with the
  main mass of water. The fire in their body merges and coalesces with
  the main mass of fire. The air in their body merges and coalesces with
  the main mass of air. The faculties are transferred to space. Four men
  with a bier carry away the corpse. Their footprints show the way to
  the cemetery. The bones become bleached. Offerings dedicated to the
  gods end in ashes. Giving is a doctrine of morons. When anyone affirms
  a positive teaching it’s just baseless, false nonsense. Both the
  foolish and the astute are annihilated and destroyed when their body
  breaks up, and don’t exist after death’?” 

The truth there is that there is no permanent , unchanging self.  What is happening is Clinging to forms,feelings,perceptions,consciousness and/or volitional formations. These Clingings are not unconditional. Craving gives rise to clinging. This is the midddle way. Depending upon conditions clinging ceases. Depending upon conditions clinging arises. This is the Dhamma. To those who believe in Self it would appear Self arises and ceases which is self contradictory as self is permanent and unchanging. Morality based upon the assumption that Self and body are the same results in moral nihilism. Morality based upon assumption that Self and body are different leads to moral nihilism. 
EDIT: I have found another Sutta(saṃyuktāgama 297) to support my answer.
Following quote illustrates the point I have been trying to make:

“What is the great discourse on the emptiness of dharmas? It is this:
  Because this exists, that exists; because this arises, that arises.
  That is to say: Conditioned by ignorance, activities arise; because of
  activities, consciousness arises, and so on …, and thus arises this
  whole mass of suffering.
“Regarding the statement conditioned by birth, aging-and-death arises,
  someone may ask: Who is it that ages-and-dies? To whom does
  aging-and-death belong?
“And he may answer: It is the self that ages-and-dies. Aging-and-death
  belongs to the self; aging-and-death is the self.
“To say that soul is the same thing as body, or to say that soul is
  one thing and body another, these have the same meaning, though they
  are expressed differently. For one who has the view which says that
  soul is the same thing as body, there is no point in the noble life.
  And for one who has the other view which says that soul is one thing
  and body another, there is also no point in the noble life. Following
  neither of these two extremes, the mind should move rightly toward the
  Middle Way.


8157: <p>In <a href="https://suttacentral.net/sn24.5/en/sujato" rel="nofollow noreferrer">SN 24.5</a>, the Lord Buddha criticized the following doctrine called "<a href="https://suttacentral.net/define/natthikav%C4%81da" rel="nofollow noreferrer">natthikavādaṃ</a>": </p>

<blockquote>
  <p><em>There is no benefit in giving, sacrifice or offerings. There’s no fruit or result of good and bad deeds. There is not this world or the
  other world. There are no duties to mother and father. No beings are
  reborn spontaneously. And there’s no ascetic or brahmin who is well
  attained and practiced, and who describes this world and the other
  world after realizing it with their own insight.</em></p>
  
  <p><em>This person is made up of the four primary elements. When they die, the earth in their body merges and coalesces with the main mass of
  earth. The water in their body merges and coalesces with the main mass
  of water. The fire in their body merges and coalesces with the main
  mass of fire. The air in their body merges and coalesces with the main
  mass of air.</em></p>
  
  <p><em>The faculties are transferred to space. Four men with a bier carry away the corpse. Their footprints show the way to the cemetery. The
  bones become bleached. Offerings dedicated to the gods end in ashes.
  Giving is a doctrine of morons. When anyone affirms a positive
  teaching (atthikavādaṃ) it’s just baseless, false nonsense. Both the
  foolish and the astute are annihilated and destroyed when their body
  breaks up and don’t exist after death.</em></p>
</blockquote>

<p>According to <a href="https://suttacentral.net/sn24.5/en/sujato" rel="nofollow noreferrer">SN 24.5</a>, why did the Lord Buddha criticize natthikavādaṃ (the doctrine of disbelief)? </p>
 471: <p>There is a related sutta, <a href="https://www.accesstoinsight.org/tipitaka/sn/sn44/sn44.006.than.html" rel="nofollow noreferrer">SN44.6</a> that says:</p>

<blockquote>
  <p>"For one who loves form (and the rest of the five aggregates), who is
  fond of form, who cherishes form, who does not know or see, as it
  actually is present, the cessation of form, there occurs the thought,
  'The Tathagata exists after death' or 'The Tathagata does not exist
  after death' or 'The Tathagata both exists and does not exist after
  death' or 'The Tathagata neither exists nor does not exist after
  death.'</p>
  
  <p>"But for one who doesn't love form (and the rest of the five
  aggregates), who isn't fond of form, who doesn't cherish form, who
  knows &amp; sees, as it actually is present, the cessation of form, the
  thought, 'The Tathagata exists after death' or 'The Tathagata does not
  exist after death' or 'The Tathagata both exists and does not exist
  after death' or 'The Tathagata neither exists nor does not exist after
  death' doesn't occur.</p>
  
  <p>"For one who loves becoming, who is fond of
  becoming, ...</p>
  
  <p>"But for one who doesn't love becoming, who isn't fond of becoming ...</p>
  
  <p>"For one who loves clinging/sustenance ...</p>
  
  <p>"But for one who doesn't love clinging/sustenance ...</p>
  
  <p>"For one who loves craving ...</p>
  
  <p>"But for one who doesn't love craving ...</p>
</blockquote>

<p>I have heard another story about a master saying "think about monkeys", and the meditator thinks about monkeys with his eyes closed. After this, the master says "don't think about monkeys", and again, the meditator never fails to think about monkeys with his eyes closed. Why? Because in both cases, he has an obsession with monkeys.</p>

<p>Similarly, views about whether 'The Tathagata exists after death' or 'The Tathagata does not exist after death' or 'The Tathagata both exists and does not exist after death' or 'The Tathagata neither exists nor does not exist after death' all occur only if one has an obsession with the five aggregates, becoming, craving and clinging.</p>

<p>Similarly, having views about whether one (the self) 'exists after death' or 'does not exist after death' or 'both exists and does not exist after death' or 'neither exists nor does not exist after death' are all due to obsession with the five aggregates, becoming, craving and clinging.</p>

<p>The <a href="http://www.accesstoinsight.org/tipitaka/sn/sn12/sn12.017.than.html" rel="nofollow noreferrer">Acela Sutta</a> shows that the Buddha teaches the Right View using <a href="https://buddhism.stackexchange.com/q/48/471">dependent origination</a>, rather than eternalism or annihilationism. (This comes from <a href="http://www.accesstoinsight.org/lib/authors/various/wheel202.html#theravada" rel="nofollow noreferrer">here</a> but the full text can be found <a href="http://www.accesstoinsight.org/tipitaka/sn/sn12/sn12.017.than.html" rel="nofollow noreferrer">here</a>):</p>

<blockquote>
  <p>Again, when the Buddha was asked by the naked ascetic Kassapa whether
  suffering was of one's own making or of another's or both or neither,
  the Buddha replied "Do not put it like that." When asked whether there
  was no suffering or whether the Buddha neither knew nor saw it, the
  Buddha replied that there was, and that he both knew and saw it. He
  then said "Kassapa, if one asserts that 'He who makes (it) feels (it):
  being one existent from the beginning, his suffering is of his own
  making,' then one arrives at eternalism. But if one asserts that one
  makes (it), another feels (it); being one existent crushed out by
  feeling, his suffering is of another's making,' then one arrives at
  annihilationism. Instead of resorting to either extreme a Tathaagata
  teaches the Dhamma by the middle way (by <a href="https://buddhism.stackexchange.com/q/48/471">dependent origination</a>)"
  (S. XII, 17/vol. ii, 20).</p>
</blockquote>

<p>The <a href="https://www.accesstoinsight.org/tipitaka/sn/sn22/sn22.085.than.html" rel="nofollow noreferrer">Yamaka Sutta</a> also speaks of an interesting notion:</p>

<blockquote>
  <p>"Then, friend Yamaka, how would you answer if you are thus asked: A
  monk, a worthy one, with no more mental effluents: what is he on the
  break-up of the body, after death?"</p>
  
  <p>"Thus asked, I would answer, 'Form is inconstant... Feeling...
  Perception... Fabrications... Consciousness is inconstant. That which
  is inconstant is stressful. That which is stressful has ceased and
  gone to its end."</p>
  
  <p>"Very good, my friend Yamaka. Very good.</p>
</blockquote>

<p>So, rather than saying that after Parinibbana, the Buddha exists or does not exist, it's better to say suffering has ceased and gone to its end.</p>

<p>In a similar way, rather than saying that after death, whether an unenlightened person is non-existent or existent or reborn or not reborn, it's better to say that suffering has not ceased. And what happens when suffering has not ceased, is understood using dependent origination.</p>
 43: <h2>Why did the Buddha criticize <em>natthika</em> (moral nihilism)?</h2>

<p>Well, it is wrong on many levels:</p>

<ol>
<li>objectively, moral nihilism leads to careless behavior, which often leads to conflict and suffering.</li>
<li>subjectively, adhering to good morals is a nice rule of thumb for reducing mental afflictions - while moral nihilism would give free reign to the blinding passions.</li>
<li>Right Dharma by its very nature has to be based on reality of how things work - and being based on how things work means its principles can be observed throughout a wide range of human activities - which is why worldly ethics and Buddhism go along 90% of the way. Moral nihilism goes contrary to worldly ethics, which means it's not in accord with how things work.</li>
<li>the entire Buddhist path is based on the idea that some states of existence are "better" (more peaceful) then others, Nirvana being "the best", with better behavior leading to better states, and better views leading to better behavior. Dharma is that "better view". To claim that moral nihilism is the right teaching would imply that moral nihilism is a better view, which is logically inconsistent, since from the standpoint of moral nihilism there cannot be such thing as "better view".</li>
<li>our ideas and results of our actions continue to exist after our death. So whatever we do has influence beyond this life, just like we have inherited actions of previous generations. Moral nihilism denies this factor, this denial being obviously false. </li>
</ol>

<p>How is this reconciled with the highest (Mahayana's) teaching of emptiness? Emptiness, or groundlessness as it is sometimes called, does NOT mean there is no good &amp; bad. It does NOT mean there's no skillful &amp; unskillful behavior. It means good/bad and skillful/unskillful cannot be simply generalized and reified. This is known even from the modern ethics with its infamous trolley problem. Good &amp; bad is not something you can decide once-and-for-all and always go by the same rule. Same goes for skillful/unskillful. If being wise and skillful were as simple as learning a rule of thumb, everyone would be a buddha by now.</p>

<p>It also involves clear understanding that, in any kind of dispute, to be too attached to one position as "the only good" - is not good, because it leads to trouble. Attachment to reified morals, aversion based on that attachment, and conflict it generates - is not the most skillful approach. It is better than having no clue, sure - but not as good as seeing the situation from all perspectives at once.</p>

<p>So from Mahayana perspective, moral categories are not tangible, they cannot be grasped. Morals and wisdom is a skill one has to master, and the more someone masters it, the more nuanced and less stereotyped it gets, until it's almost like it has no definite shape - and yet you can see it working with clarity.</p>

<p>At the very end of this progression of mastery is what Mahayana calls groundlessness or positionlessness of a great master. Nothing can be further away from the moral nihilism.</p>
 11541: <p>The answer is present in the same sutta:</p>

<blockquote>
  <p>“When form exists, because of grasping form and insisting on form, the
  view arises: ‘There’s no meaning in giving, sacrifice, or offerings. …
  Both the foolish and the astute are annihilated and destroyed when
  their body breaks up, and don’t exist after death.’ When feeling …
  perception … choices … consciousness exists, because of grasping
  consciousness and insisting on consciousness, the view arises:
  ‘There’s no meaning in giving, sacrifice, or offerings. … Both the
  foolish and the astute are annihilated and destroyed when their body
  breaks up, and don’t exist after death.’</p>
</blockquote>

<p>In other words when self identification with forms,feelings,perception,consciousness and/or volitional formations occur such a view as highlighted by you also occurs.</p>

<p>I think the the wrong view of moral nihilism gets generated when we say that every self ceases to exist after death(i.e body and self are same) or that every self lives for eternity(i.e body and self are different). In both the case following holds true :</p>

<blockquote>
  <p>‘There’s no meaning in giving, sacrifice, or offerings. There’s no
  fruit or result of good and bad deeds. There’s no afterlife. There are
  no duties to mother and father. No beings are reborn spontaneously.
  And there’s no ascetic or brahmin who is well attained and practiced,
  and who describes the afterlife after realizing it with their own
  insight. This person is made up of the four primary elements. When
  they die, the earth in their body merges and coalesces with the main
  mass of earth. The water in their body merges and coalesces with the
  main mass of water. The fire in their body merges and coalesces with
  the main mass of fire. The air in their body merges and coalesces with
  the main mass of air. The faculties are transferred to space. Four men
  with a bier carry away the corpse. Their footprints show the way to
  the cemetery. The bones become bleached. Offerings dedicated to the
  gods end in ashes. Giving is a doctrine of morons. When anyone affirms
  a positive teaching it’s just baseless, false nonsense. Both the
  foolish and the astute are annihilated and destroyed when their body
  breaks up, and don’t exist after death’?” </p>
</blockquote>

<p>The truth there is that there is no permanent , unchanging self.  What is happening is Clinging to forms,feelings,perceptions,consciousness and/or volitional formations. These Clingings are not unconditional. Craving gives rise to clinging. This is the midddle way. Depending upon conditions clinging ceases. Depending upon conditions clinging arises. This is the Dhamma. To those who believe in Self it would appear Self arises and ceases which is self contradictory as self is permanent and unchanging. Morality based upon the assumption that Self and body are the same results in moral nihilism. Morality based upon assumption that Self and body are different leads to moral nihilism. </p>

<p>EDIT: I have found another Sutta(<a href="https://suttacentral.net/sa297/en/choong" rel="nofollow noreferrer">saṃyuktāgama 297</a>) to support my answer.
Following quote illustrates the point I have been trying to make:</p>

<blockquote>
  <p>“What is the great discourse on the emptiness of dharmas? It is this:
  Because this exists, that exists; because this arises, that arises.
  That is to say: Conditioned by ignorance, activities arise; because of
  activities, consciousness arises, and so on …, and thus arises this
  whole mass of suffering.</p>
  
  <p>“Regarding the statement conditioned by birth, aging-and-death arises,
  someone may ask: Who is it that ages-and-dies? To whom does
  aging-and-death belong?</p>
  
  <p>“And he may answer: It is the self that ages-and-dies. Aging-and-death
  belongs to the self; aging-and-death is the self.</p>
  
  <p>“To say that soul is the same thing as body, or to say that soul is
  one thing and body another, these have the same meaning, though they
  are expressed differently. For one who has the view which says that
  soul is the same thing as body, there is no point in the noble life.
  And for one who has the other view which says that soul is one thing
  and body another, there is also no point in the noble life. Following
  neither of these two extremes, the mind should move rightly toward the
  Middle Way.</p>
</blockquote>
