It was a bad idea to design society around two ridiculous, commedia dell'arte-esque character archetypes and then just build that into absolutely everything.
Tangential point - I believe the unthinking assumption and expectation for it to be everywhere is a big part of what keeps us from moving foreward on other aspects of how we're handling it. The angry public contention about who is allowed into what institutions could be solved in an instant if people would just step back and ask themselves "do we really need separate institutions?" and "do they need to be separated along these specific lines?". Every time I read about where people are arguing about who's allowed in which sports teams I find myself shouting at the screen "organize the teams by weight class!"; but nobody on either side of the argument ever comes to that conclusion because nobody on either side has bothered to question the underlaying assumption that the division will necessarily be that there will be a men's league and a women's league