Or maybe - and call me crazy here - men and women are different, and want different things, and therefore, as we reduce discrimination, nearly every job and hobby will end up with a huge gender imbalance as individuals sort themselves into groups doing what they truly, freely want to do.

Then your conviction that every job must be exactly 50% of each gender no matter how much power must be wielded to make it happen would be a massively misguided recipe for tyranny, harming both men and women.