> So will the government mandate that 50% of stay at home parents be men?

Well, obviously not. But there is always the caveat that suggesting government providing adequate child care to working women is communism of whatever. Is it feasible to have some compromise here?

> And if 50/50 is the goal, where is the government push for more men in places where they're underrepresented, like university students, nurses, teachers?

This sounds like a perfectly legitimate ask if young men do really care about it. Why not contact your local representative and explain the issue in an articulate manner?