I think YOU'RE missing the point. Childcare is still considered a less important and honorable occupation than pretty much everything else you can do. If you're "just" a parent, you're not considered qualified for really anything else.

That means most men won't do it, because they'll lose status. Meanwhile women will always place lower importance on status than on childcare, and so they will do childcare because no one is available to do it for them.

The disparity won't ever disappear until it's just as valid and socially supported for a man to stay home and raise children, as for a woman.