user19335: Every now and then we (close friends) start some discussion on some topic, then we put our sides, but unfortunately, this conversation takes a path towards argument, where both the sides want to prove that they are correct. This is forcing me to not to start any type of conversation among us in future because I don't want to hamper my peace of mind.
What should be the right suggestion over here? Shall we dig deeper into the conversations more and more, and until the conclusion does not comes up, just don't stop. Or, just tell your friend that you are right, and try to wrap the conversation over there itself. Or is there any other good way to reaching out to a pleasant end?

user-1: Arguing could be related or equal to grasping a view (ditthupadana) by telling ourselves that our own view is the right way to go.
Getting into arguments could also be considered grasping a perception of one self (attavadupadana) by perceiving ourselves as right.
From MN11:

There are these four kinds of grasping. What four? Grasping at sensual pleasures, views, precepts and observances, and theories of a self.
...
When that mendicant has given up ignorance and given rise to knowledge, they don’t grasp at sensual pleasures, views, precepts and observances, or theories of a self. Not grasping, they’re not anxious. Not being anxious, they personally become extinguished.

https://suttacentral.net/mn11/en/sujato
Based on the above, for your own - and others sake - there isn't much point in trying to coerce others. It doesn't do any good to any of you.

user471: From Sutta Nipata 4.11:

"From where have there arisen quarrels, disputes, lamentation,
sorrows, along with selfishness, conceit & pride, along with
divisiveness? From where have they arisen?    Please tell me."
"From what is dear there have arisen quarrels, disputes, lamentation,
sorrows, along with selfishness, conceit & pride, along with
divisiveness. Tied up with selfishness are quarrels & disputes. In the
arising of disputes is divisiveness."

Basically you have things dear to you and your friend has things dear to him or her. "Dear" here means clinging or attachment. For e.g. you cling to your religion and political ideology, while your friend clings to his or her religion and political ideology. This difference causes the arising of quarrels and disputes.
The best thing to do is just agree to disagree, out of friendliness or kindness. That should settle the quarrel.
In MN 128, the Buddha gave this advice:

For enmity in this world
is never settled by enmity.
It’s only settled by love:
this is an ancient principle.
Others don’t understand
that our lives must have limits.
The clever ones who know this
settle their quarrels right away.

The word that was translated as "love" above is avera in Pali, which is translated by some dictionaries as friendliness or kindness.

user2282: 
What should be the right suggestion over here? Shall we dig deeper into the conversations more and more, and until the conclusion does not comes up, just don't stop. Or, just tell your friend that you are right, and try to wrap the conversation over there itself. Or is there any other good way to reaching out to a pleasant end?

There's no one-size-fits-all solution here because it all depends on the content of the conversation. If your friend advocates some kind of wrong view that affects the safety or well-being of himself and/or others ( ex: advocating smoking/drinking/endulging in sensual pleasures as beneficial, advocating unrestraints in stealing, lying, cheating, abusive bodily/verbally toward others, etc... ), then you'll have to be firm and clear in stating your disagreement, even when knowing that your friend will never change his wrong view.

user-1: If it gets out of hand i consider whether they are fit to talk to. If they are unfit to talk to, not up to sutta standards i don't talk to them at all or i narrow the range of communication.

"Monks, it's through his way of participating in a discussion that a person can be known as fit to talk with or unfit to talk with. If a person, when asked a question, doesn't give a categorical answer to a question deserving a categorical answer, doesn't give an analytical (qualified) answer to a question deserving an analytical answer, doesn't give a counter-question to a question deserving a counter-question, doesn't put aside a question deserving to be put aside, then — that being the case — he is a person unfit to talk with. But if a person, when asked a question, gives a categorical answer to a question deserving a categorical answer, gives an analytical answer to a question deserving an analytical answer, gives a counter-question to a question deserving a counter-question, and puts aside a question deserving to be put aside, then — that being the case — he is a person fit to talk with.
"Monks, it's through his way of participating in a discussion that a person can be known as fit to talk with or unfit to talk with. If a person, when asked a question, doesn't stand by what is possible and impossible, doesn't stand by agreed-upon assumptions, doesn't stand by teachings known to be true,[1] doesn't stand by standard procedure, then — that being the case — he is a person unfit to talk with. But if a person, when asked a question, stands by what is possible and impossible, stands by agreed-upon assumptions, stands by teachings known to be true, stands by standard procedure, then — that being the case — he is a person fit to talk with.
"Monks, it's through his way of participating in a discussion that a person can be known as fit to talk with or unfit to talk with. If a person, when asked a question, wanders from one thing to another, pulls the discussion off the topic, shows anger & aversion and sulks, then — that being the case — he is a person unfit to talk with. But if a person, when asked a question, doesn't wander from one thing to another, doesn't pull the discussion off the topic, doesn't show anger or aversion or sulk, then — that being the case — he is a person fit to talk with.
"Monks, it's through his way of participating in a discussion that a person can be known as fit to talk with or unfit to talk with. If a person, when asked a question, puts down [the questioner], crushes him, ridicules him, grasps at his little mistakes, then — that being the case — he is a person unfit to talk with. But if a person, when asked a question, doesn't put down [the questioner], doesn't crush him, doesn't ridicule him, doesn't grasp at his little mistakes, then — that being the case — he is a person fit to talk with.
"Monks, it's through his way of participating in a discussion that a person can be known as drawing near or not drawing near. One who lends ear draws near; one who doesn't lend ear doesn't draw near. Drawing near, one clearly knows one quality, comprehends one quality, abandons one quality, and realizes one quality.[2] Clearly knowing one quality, comprehending one quality, abandoning one quality, and realizing one quality, one touches right release. For that's the purpose of discussion, that's the purpose of counsel, that's the purpose of drawing near, that's the purpose of lending ear: i.e., the liberation of the mind through no clinging. https://www.accesstoinsight.org/tipitaka/an/an03/an03.067.than.html

It is my impression that some people aren't used to a formal format of discussion but do come around embracing the due process.
In general if people want to discuss something i evaluate whether they actually want to get to the bottom of it, if they are willing to have their views challenged and whether they will respect my time and the process.
These things are non negotiable. I do my best and expect others to do their best but if it's too stressful and is not yielding worthy results, then i just don't engage them.
If people appreciate talking to you and your demands are reasonable then  losing access to you is a more or less of a bad outcome for them, if they realize this they might try harder. If otherwise you let people argue they are likely to just keep at it, it's my general impression.
Other aspects of this is our own behavior and the choice of topics. Some things are hard to express correctly and the timing for the expression is crucial.
It is very hard to get these things right, to make one's point step by step and in due time. Therefore one shouldn't just cut people off hastly and one should take responsibility to improve what can be improved.

19335: <p>Every now and then we (close friends) start some discussion on some topic, then we put our sides, but unfortunately, this conversation takes a path towards argument, where both the sides want to prove that they are correct. This is forcing me to not to start any type of conversation among us in future because I don't want to hamper my peace of mind.</p>
<p>What should be the right suggestion over here? Shall we dig deeper into the conversations more and more, and until the conclusion does not comes up, just don't stop. Or, just tell your friend that you are right, and try to wrap the conversation over there itself. Or is there any other good way to reaching out to a pleasant end?</p>
 -1: <p>Arguing could be related or equal to grasping a view (ditthupadana) by telling ourselves that <strong>our own view</strong> is the right way to go.</p>
<p>Getting into arguments could also be considered grasping a perception of one self (attavadupadana) by perceiving <strong>ourselves as right</strong>.</p>
<p>From MN11:</p>
<blockquote>
<p>There are these four kinds of grasping. What four? Grasping at sensual pleasures, <strong>views</strong>, precepts and observances, and <strong>theories of a self</strong>.</p>
<p>...</p>
<p>When that mendicant has given up ignorance and given rise to knowledge, they don’t grasp at sensual pleasures, views, precepts and observances, or theories of a self. Not grasping, they’re not anxious. Not being anxious, they personally become extinguished.</p>
</blockquote>
<p><a href="https://suttacentral.net/mn11/en/sujato" rel="nofollow noreferrer">https://suttacentral.net/mn11/en/sujato</a></p>
<p>Based on the above, for your own - and others sake - there isn't much point in trying to coerce others. It doesn't do any good to any of you.</p>
 471: <p>From <a href="https://www.accesstoinsight.org/tipitaka/kn/snp/snp.4.11.than.html" rel="nofollow noreferrer">Sutta Nipata 4.11</a>:</p>
<blockquote>
<p>&quot;From where have there arisen quarrels, disputes, lamentation,
sorrows, along with selfishness, conceit &amp; pride, along with
divisiveness? From where have they arisen?    Please tell me.&quot;</p>
<p>&quot;From what is dear there have arisen quarrels, disputes, lamentation,
sorrows, along with selfishness, conceit &amp; pride, along with
divisiveness. Tied up with selfishness are quarrels &amp; disputes. In the
arising of disputes is divisiveness.&quot;</p>
</blockquote>
<p>Basically you have things dear to you and your friend has things dear to him or her. &quot;Dear&quot; here means clinging or attachment. For e.g. you cling to your religion and political ideology, while your friend clings to his or her religion and political ideology. This difference causes the arising of quarrels and disputes.</p>
<p>The best thing to do is just agree to disagree, out of friendliness or kindness. That should settle the quarrel.</p>
<p>In <a href="https://suttacentral.net/mn128/en/sujato" rel="nofollow noreferrer">MN 128</a>, the Buddha gave this advice:</p>
<blockquote>
<p>For enmity in this world<br />
is never settled by enmity.<br />
<strong>It’s only settled by love:</strong><br />
this is an ancient principle.</p>
<p>Others don’t understand<br />
that our lives must have limits.<br />
The clever ones who know this<br />
<strong>settle their quarrels right away</strong>.</p>
</blockquote>
<p>The word that was translated as &quot;love&quot; above is <em><a href="http://dictionary.sutta.org/browse/a/avera" rel="nofollow noreferrer">avera</a></em> in Pali, which is translated by some dictionaries as friendliness or kindness.</p>
 2282: <blockquote>
<p>What should be the right suggestion over here? Shall we dig deeper into the conversations more and more, and until the conclusion does not comes up, just don't stop. Or, just tell your friend that you are right, and try to wrap the conversation over there itself. Or is there any other good way to reaching out to a pleasant end?</p>
</blockquote>
<p>There's no one-size-fits-all solution here because it all depends on the content of the conversation. If your friend advocates some kind of wrong view that affects the safety or well-being of himself and/or others ( ex: advocating smoking/drinking/endulging in sensual pleasures as beneficial, advocating unrestraints in stealing, lying, cheating, abusive bodily/verbally toward others, etc... ), then you'll have to be firm and clear in stating your disagreement, even when knowing that your friend will never change his wrong view.</p>
 -1: <p>If it gets out of hand i consider whether they are fit to talk to. If they are unfit to talk to, not up to sutta standards i don't talk to them at all or i narrow the range of communication.</p>
<blockquote>
<p>&quot;Monks, it's through his way of participating in a discussion that a person can be known as fit to talk with or unfit to talk with. If a person, when asked a question, doesn't give a categorical answer to a question deserving a categorical answer, doesn't give an analytical (qualified) answer to a question deserving an analytical answer, doesn't give a counter-question to a question deserving a counter-question, doesn't put aside a question deserving to be put aside, then — that being the case — he is a person unfit to talk with. But if a person, when asked a question, gives a categorical answer to a question deserving a categorical answer, gives an analytical answer to a question deserving an analytical answer, gives a counter-question to a question deserving a counter-question, and puts aside a question deserving to be put aside, then — that being the case — he is a person fit to talk with.</p>
<p>&quot;Monks, it's through his way of participating in a discussion that a person can be known as fit to talk with or unfit to talk with. If a person, when asked a question, doesn't stand by what is possible and impossible, doesn't stand by agreed-upon assumptions, doesn't stand by teachings known to be true,[1] doesn't stand by standard procedure, then — that being the case — he is a person unfit to talk with. But if a person, when asked a question, stands by what is possible and impossible, stands by agreed-upon assumptions, stands by teachings known to be true, stands by standard procedure, then — that being the case — he is a person fit to talk with.</p>
<p>&quot;Monks, it's through his way of participating in a discussion that a person can be known as fit to talk with or unfit to talk with. If a person, when asked a question, wanders from one thing to another, pulls the discussion off the topic, shows anger &amp; aversion and sulks, then — that being the case — he is a person unfit to talk with. But if a person, when asked a question, doesn't wander from one thing to another, doesn't pull the discussion off the topic, doesn't show anger or aversion or sulk, then — that being the case — he is a person fit to talk with.</p>
<p>&quot;Monks, it's through his way of participating in a discussion that a person can be known as fit to talk with or unfit to talk with. If a person, when asked a question, puts down [the questioner], crushes him, ridicules him, grasps at his little mistakes, then — that being the case — he is a person unfit to talk with. But if a person, when asked a question, doesn't put down [the questioner], doesn't crush him, doesn't ridicule him, doesn't grasp at his little mistakes, then — that being the case — he is a person fit to talk with.</p>
<p>&quot;Monks, it's through his way of participating in a discussion that a person can be known as drawing near or not drawing near. One who lends ear draws near; one who doesn't lend ear doesn't draw near. Drawing near, one clearly knows one quality, comprehends one quality, abandons one quality, and realizes one quality.[2] Clearly knowing one quality, comprehending one quality, abandoning one quality, and realizing one quality, one touches right release. For that's the purpose of discussion, that's the purpose of counsel, that's the purpose of drawing near, that's the purpose of lending ear: i.e., the liberation of the mind through no clinging. <a href="https://www.accesstoinsight.org/tipitaka/an/an03/an03.067.than.html" rel="nofollow noreferrer">https://www.accesstoinsight.org/tipitaka/an/an03/an03.067.than.html</a></p>
</blockquote>
<p>It is my impression that some people aren't used to a formal format of discussion but do come around embracing the due process.</p>
<p>In general if people want to discuss something i evaluate whether they actually want to get to the bottom of it, if they are willing to have their views challenged and whether they will respect my time and the process.</p>
<p>These things are non negotiable. I do my best and expect others to do their best but if it's too stressful and is not yielding worthy results, then i just don't engage them.</p>
<p>If people appreciate talking to you and your demands are reasonable then  losing access to you is a more or less of a bad outcome for them, if they realize this they might try harder. If otherwise you let people argue they are likely to just keep at it, it's my general impression.</p>
<p>Other aspects of this is our own behavior and the choice of topics. Some things are hard to express correctly and the timing for the expression is crucial.</p>
<p>It is very hard to get these things right, to make one's point step by step and in due time. Therefore one shouldn't just cut people off hastly and one should take responsibility to improve what can be improved.</p>
