2 Apes naturally favour gendered toys and the most egalitarian countries have high discrepancies in interest, that's outright false.
3 Nobody's encouraged to be a professional sportsman, it's a dreamer career that requires self-motivation until you can display competitive performance.
4 It's not though.
Give me the money for it and I will.
I know the study you're talking about, did you even read it? That study found that MALE MONKEYS (not apes, btw, the study was on macaques) have a preference for gendered toys. Females do not. But we are not talking about rhesus macaques, are we?
That is patently false. Professional chess players are typically introduced to chess at a young age and encouraged to compete in chess at a young age, usually by one or both parents. You might have noticed that trend if you actually knew anything about professional chess players. Oh, and btw... getting into sports? That costs money. Who pays for you to get into sports at a young age? Your parents. My second sister got into classical ballet because my parents encouraged all of us to try it out, and she enjoyed it so my parents continued to pay for her dancing classes and encourage her to dance. And yes, it's like this for almost every single person on the planet. No, it's not the only factor, but it's a huge one, and that you would try to argue that it's not a factor at all is laughable.
It is, though. Someone has to pay for those chessboards. Someone has to take time and/or money for lessons and competitions. I'm starting to think you're being deliberately obtuse on this.