The "boys rule, girls drool" trope can be enacted anywhere and everywhere. And it is. Everywhere. Just read Calvin & Hobbes! It's presented as... humor!
It requires no difference in skin color, class, or anything else. Just gender. The children are educated that some people are more important, and others are less so. And this is the place where dominance through violence takes root.
Men are taught to disconnect, compete, and win. Women are taught to submit, collaborate, and serve.
But as you say, if we can get down to the root of the rot, maybe we can start to do something productive about it.
As it is, you've done a masterful job of illuminating exactly what the women (who can) are screaming so loudly about these days. Thank you.