I agree 100 percent with your overall point, but I do want to comment on the part where you point out that women are still underrepresented in politics and that girls drop out of sports. I believe that statistics show that in the most egalitarian countries, where men and women have the narrowest pay gaps and the most equal standing legally, women end up choosing to stay at home and work part time more often than in comparably rich but not as egalitarian countries. Women do have different priorities and likes (on average, of course). I don't have the data for this, but I suspect that a lot of girls choose not to continue with sports because their priorities change, and that's ok. I also suspect more men than women enjoy the competitive and often combative and aggressive side of politics. That's where the difficulty arises oftentimes - in the murkiness of predispositions versus stereotypes.