I offer an a priori argument that women do not prioritize their children over their relationship satisfaction using the most egalitarian nations and increases in rates of divorce these nations have over more patriarchal societies, using the United States as the comparison metric.

Simply stated, as a nation becomes more egalitarian, we expect that the number of children who grow up in the house of their father decreases since divorce increases.

If this phenomenon was reversed, and more patriarchal nations led to an increase in divorce rates then we would expect a set of reflexive arguments to appear.

The reflexive response to this, which is factually incorrect, is that women aren't able to divorce in these nations. But we're merely speaking of developed first world nations with low exit barriers to marriage. And in fact, in nations where divorce can be initiated through the internet, such a low exit barrier does not increase divorces.

So from that, we can conclude, that the divorces that do occur, are because the person actually wants to get divorced, and within both nation structures, such a thing is easily accessible (we are excluding any nations where women are not allowed to freely divorce their partners).

We would also expect arguments that women are escaping "abusive relationships" in these patriarchal nations. And so conversely, we should expect these arguments then don't hold water.

Restated

(Patriarchy)The nuclear family is not a female value system.

Facts

• Egalitarian nations have higher divorce rates
• As egalitarian values have taken root, women have begun to lag men in happiness (female happiness paradox)
• Nations highest in egalitarian values, lack, or have markedly lower social stigmas for women to have families outside of wedlock.
• Children who grow with single mothers have markedly poorer outcomes
• Most relationships are not abusive. Therefor it would be unreasonable to conclude that instead these women are just more free to leave abusive relationships.
• Since having children outside of wedlock is not stigmatized or markedly less so, men and women who value marriage and the nuclear family the least, have self selected out of the pool of possible divorcees.

Fair assumptions

• Nations that are more egalitarian should produce men who treat women better, or else, such nations wouldn't be "more egalitarian."
• Most women are innately (or at least subconsciously) aware of the impact a divorce will have on their children. Therefor it would be unreasonable to assume that most of these women believe they are doing the right thing for the children.

Therefor we can conclude

• As a country becomes more feminine, the number of children who will grow up in the house of their father decreases.
• Women will prioritize their relationships, over their children's well being.
• And be less happy, while doing it. (female happiness paradox)

I conclude that it is reasonable to deduce that a society that prioritizes egalitarian values and allows women to operate in ways that "makes them the happiest" will have a negative impact on children and the very women who believe it will make them the happiest (female happiness paradox).

Alternative proof

If the well being of their children were a priority for most women, then the number of divorces would decrease for two reasons.

1. They are getting "what they want" (egalitarian relationships & partners)
2. Since an intact nuclear family is innately obvious as a benefit to the child, she would prioritize this, over a new relationship (since it is unlikely such a change was because she was forced to choose a male lacking nurturing qualities, escape an abusive relationship)

Caveat (converse to fair assumptions)

• Do women not actually understand the impact of separation on children? Does it need to be taught that such a thing is damaging to their children.
• Are feminine men, and egalitarian values not making women happy with their partners or their lives?

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Satire is often a good source of pointing out the baseline phenomenon and exposing it for what it really is, and TL;DR, I think this was best brought to light by Southpark. Though such a view could be male biased (then reference caveat).

Mrs Marsh: Stanley, you know you’re the most important thing in the world to me, right?

Stan: If that’s true then get back together with Dad for me.

Mrs. Marsh: Now Stanley, you have to understand how divorce works. When I say you’re the most important thing to me, what I mean is you’re the most important thing after me and my happiness and my new romances.