Some of that is false, but not all of it. And some of it is misleading.
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.