In the US, many states have family court systems with statutory and/or systemic biases against fathers. Mothers are typically given majority custody of the children and deference when it comes to making decisions about the children.
Single mothers often qualify for government assistance that they wouldn't qualify for as a married woman. Tax credits and deductions are awarded to the parent with majority custody (which is typically women).
Fathers typically contribute more to the financial assets of the marriage, yet are typically lucky to receive 50% of marital assets in a divorce. Men typically have higher long-term earnings than women in the US (for reasons that aren't discriminatory), and courts typically award the lower earning spouse some percentage of the higher-earning spouses future income in a divorce (even when there aren't children).
When it comes to paying for costs related to raising children (school tuition, sports, fees, medical costs), the higher earning spouse is typically ordered to pay a higher proportion of the costs (like 60-70%).
For example, women usually get more custody, but that’s also because men often don’t seek custody. Men who seek custody are awarded it at similar rates as women, IIRC.
It’s also not true that men are “lucky” to get 50% of the assets. That’s the default position in community property states.
And it still doesn’t explain how women are incentivized to divorce, given that despite some of the things above, women still fare worse in divorce than men do. Child support and alimony are, on average, something like softens the blow for the lower-earning spouse, not a path to a higher standard of living than was enjoyed in the marriage.
FWIW, I’m divorced and pay child support and the lion’s share of kid expenses, including school tuition. And yet I wouldn’t trade my financial position for my ex’s. This is true for almost every divorced man I know, and I know a lot at this point.