user471: What could be the purpose of the Buddha teaching AN 2.61 below? Why is this relevant? How is this useful?
AN 2.61 states:

“Mendicants, females die without getting enough of two things.
“Dvinnaṃ dhammānaṃ, bhikkhave, atitto appaṭivāno mātugāmo kālaṃ
  karoti.
What two?
Katamesaṃ dvinnaṃ?
Sexual intercourse and giving birth.
Methunasamāpattiyā ca vijāyanassa ca.
Females die without getting enough of these two things.”
Imesaṃ kho, bhikkhave, dvinnaṃ dhammānaṃ atitto appaṭivāno mātugāmo kālaṃ
  karotī”ti.


user-1: Good householder, interested,
A teaching to monks on their biggest danger, the female (as in many teaching to keep them careful and in good distance to fire for them): To develope on one hand compassion and goodwill, avoid tendencies which lead to femal circumstances for one self, and to don't oriented, walk after, femal in general, as well as stay aware of the danger of improper assosiation beyond giving out of compassion useful for the path. 
One might know that most of the womans-attribut-teachings had been taught toward Ven. Ananda, who cleared had been very attached to female and tended to sacrifice his own practice for the sake of womans issues. It's also clear that one encounters dangers best right on the high peak.
Further: Sex should also be understood in all of it's kind, with union with devas on the top refined, or just socialicing. Giving birth means to desire (control, owning of offsprings). It would be possible likewise taught to nuns, yet not done to do not confuse hierarchy and orders. 
On sex, copling: Methuna Sutta: The Discourse on Coupling. Sex can be understood als as enteraining, nourishing, uppadana in it's deep meaning. After a nother Dhammatalk and satisfaction of desire for the bliss of understand, know, is similar pattern like seeking for sex. 
Satisfied? Or want more or again?
At least, but not to forget, as found in the Bhikkhuni Sutta, pride is used to overcome pride, and what drives a woman more to eager effort then to suggest that not matching a mans capability. 

”'This body comes into being through conceit. And yet it is by relying on conceit that conceit is to be abandoned.' Thus was it said. And in reference to what was it said? There is the case, sister, where a monk hears, 'The monk named such-and-such, they say, through the ending of the fermentations, has entered & remains in the fermentation-free awareness-release & discernment-release, having known & realized them for himself in the here & now.' The thought occurs to him, 'The monk named such-and-such, they say, through the ending of the fermentations, has entered & remains in the fermentation-free awareness-release & discernment-release, having known & realized them for himself in the here & now. Then why not me?' Then, at a later time, he abandons conceit, having relied on conceit. 'This body comes into being through conceit. And yet it is by relying on conceit that conceit is to be abandoned.' Thus was it said, and in reference to this was it said.

A strategy to enforce what ever recources of effort for the practice, which was often used by the Buddha, "You could be as free as I am, unbond, as you see, is possible. Provoting is a very effective means for motivation.

They can see even from afar. Even up close, they are invisible. With their awareness they know the minds of others. They would know this of me: "Look, my friends, at this clansman who — though he has in good faith gone forth from the home life into homelessness — remains overcome with evil, unskillful mental qualities."' So he reflects on this: 'My persistence will be aroused & not lax; my mindfulness established & not confused; my body calm & not aroused; my mind centered & unified.' AN 3.40

(Possible more and extended, at least with place to ask further and discuss, in proper and given circumastanecs for such, here: [Q&A] What purpose do "bad disriminating seeming" Sutta have, like in AN 2.61?.)
(Note that this is not given for trade exchange, stacks and other, even good seeming Sex, coupling, bound in dependency, but for liberation from desire of it)

user43: I suppose "to die without getting enough" is a colloquial expression for being insatiable, indefatigable.
This is an emphatic way of saying that women have a strong instinctual desire to bear children. If you polled a big enough sample of women I suspect majority would say they like to have children, enjoy having children, and many would say they'd want to have more then one child if allowed by the living circumstances.
The point of this in context of Buddha's teaching is that samsara has built-in mechanisms for self-continuation. Natural phenomena have innate tendency to proliferate, to continue, to support their kin, to procreate. 
Left unchecked, the stream of samsara rolls forward endlessly regenerating ignorance, confusion, desire, suffering, and desire to escape suffering. It is the ignorant pursuit of this desire is what supports the stream's momentum to roll on and on.

471: <p>What could be the purpose of the Buddha teaching AN 2.61 below? Why is this relevant? How is this useful?</p>

<p><a href="https://suttacentral.net/an2.52-63/en/sujato" rel="nofollow noreferrer">AN 2.61</a> states:</p>

<blockquote>
  <p>“Mendicants, females die without getting enough of two things.<br>
  <em>“Dvinnaṃ dhammānaṃ, bhikkhave, atitto appaṭivāno mātugāmo kālaṃ
  karoti.</em></p>
  
  <p>What two?<br>
  <em>Katamesaṃ dvinnaṃ?</em></p>
  
  <p>Sexual intercourse and giving birth.<br>
  <em>Methunasamāpattiyā ca vijāyanassa ca.</em></p>
  
  <p>Females die without getting enough of these two things.”<br>
  <em>Imesaṃ kho, bhikkhave, dvinnaṃ dhammānaṃ atitto appaṭivāno mātugāmo kālaṃ
  karotī”ti.</em></p>
</blockquote>
 -1: <p>Good householder, interested,</p>

<p>A teaching to monks on their biggest danger, the female (as in many teaching to keep them careful and in good distance to fire for them): To develope on one hand compassion and goodwill, avoid tendencies which lead to femal circumstances for one self, and to don't oriented, walk after, femal in general, as well as stay aware of the danger of improper assosiation beyond giving out of compassion useful for the path. </p>

<p>One might know that most of the womans-attribut-teachings had been taught toward Ven. Ananda, who cleared had been very attached to female and tended to sacrifice his own practice for the sake of womans issues. It's also clear that one encounters dangers best right on the high peak.</p>

<p>Further: Sex should also be understood in all of it's kind, with union with devas on the top refined, or just socialicing. Giving birth means to desire (control, owning of offsprings). It would be possible likewise taught to nuns, yet not done to do not confuse hierarchy and orders. </p>

<p>On sex, copling: <a href="https://sangham.net/en/tipitaka/sut/an/an07/an07.047.tanp" rel="nofollow noreferrer">Methuna Sutta: The Discourse on Coupling</a>. Sex can be understood als as enteraining, nourishing, uppadana in it's deep meaning. After a nother Dhammatalk and satisfaction of desire for the bliss of understand, know, is similar pattern like seeking for sex. </p>

<p>Satisfied? Or want more or again?</p>

<p>At least, but not to forget, as found in the Bhikkhuni Sutta, pride is used to overcome pride, and what drives a woman more to eager effort then to suggest that not matching a mans capability. </p>

<blockquote>
  <p>”'This body comes into being through conceit. And yet it is by relying on conceit that conceit is to be abandoned.' Thus was it said. And in reference to what was it said? There is the case, sister, where a monk hears, 'The monk named such-and-such, they say, through the ending of the fermentations, has entered &amp; remains in the fermentation-free awareness-release &amp; discernment-release, having known &amp; realized them for himself in the here &amp; now.' The thought occurs to him, 'The monk named such-and-such, they say, through the ending of the fermentations, has entered &amp; remains in the fermentation-free awareness-release &amp; discernment-release, having known &amp; realized them for himself in the here &amp; now. Then why not me?' Then, at a later time, he abandons conceit, having relied on conceit. 'This body comes into being through conceit. And yet it is by relying on conceit that conceit is to be abandoned.' Thus was it said, and in reference to this was it said.</p>
</blockquote>

<p>A strategy to enforce what ever recources of effort for the practice, which was often used by the Buddha, "You could be as free as I am, unbond, as you see, is possible. Provoting is a very effective means for motivation.</p>

<blockquote>
  <p>They can see even from afar. Even up close, they are invisible. With their awareness they know the minds of others. They would know this of me: "Look, my friends, at this clansman who — though he has in good faith gone forth from the home life into homelessness — remains overcome with evil, unskillful mental qualities."' So he reflects on this: 'My persistence will be aroused &amp; not lax; my mindfulness established &amp; not confused; my body calm &amp; not aroused; my mind centered &amp; unified.' <a href="https://zugangzureinsicht.org/html/tipitaka/an/an03/an03.040.than_en.html" rel="nofollow noreferrer">AN 3.40</a></p>
</blockquote>

<p>(Possible more and extended, at least with place to ask further and discuss, in proper and given circumastanecs for such, here: <a href="https://forum.sangham.net/index.php?topic=9824.msg22471#msg22471" rel="nofollow noreferrer">[Q&amp;A] What purpose do "bad disriminating seeming" Sutta have, like in AN 2.61?</a>.)</p>

<p><em>(Note that this is not given for trade exchange, stacks and other, even good seeming Sex, coupling, bound in dependency, but for liberation from desire of it)</em></p>
 43: <p>I suppose "to die without getting enough" is a colloquial expression for being insatiable, indefatigable.</p>

<p>This is an emphatic way of saying that women have a strong instinctual desire to bear children. If you polled a big enough sample of women I suspect majority would say they like to have children, enjoy having children, and many would say they'd want to have more then one child if allowed by the living circumstances.</p>

<p>The point of this in context of Buddha's teaching is that samsara has built-in mechanisms for self-continuation. Natural phenomena have innate tendency to proliferate, to continue, to support their kin, to procreate. </p>

<p>Left unchecked, the stream of samsara rolls forward endlessly regenerating ignorance, confusion, desire, suffering, and desire to escape suffering. It is the ignorant pursuit of this desire is what supports the stream's momentum to roll on and on.</p>
