You're also rampantly committing the naturalistic fallacy. What's natural tells us nothing about what's right. Even if we have made a perfectly fair society (which we certainly haven't) and discover that there is some difference in outcomes that is explainable by genetic differences, that doesn't mean we should accept the result.This is what's frustrating about these conversations, the worst is always assumed. Given that I absolutely do not believe that "natural" implies "right", I'm annoyed at the accusation, which comes up with some regularity even though I (like most others in the "not-only-nurture" camp) specifically disclaim such a view and never said a single thing about what is right or not.
If some people are genetically likely to be less good at math, should we cancel their math classes? Or should we give them better ones? I say the latter: as a society we want people to understand and appreciate math.
First, let me be clear: I think that the evidence that women are genetically worse at math is shoddy, at best. I think the evidence that their performance is less variable is very robust, but that's a very different claim.
Second, if either one is provably the case, then no, I very strongly don't think we should just throw our hands up. I think we should try to look at what causes the difference in statistical distribution of talent and figure out how to exploit/correct it - it's evolutionarily inconceivable that math talent is directly hard-coded genetically, so it's got to be emerging as a second or third order effect of genes, perhaps related to stress response (learning math is a process of experiencing micro-stresses over and over, and dealing with them in a way that makes you learn rather than get frustrated or angry - the "mathy" emotional state is a very delicate balance, even in people that are good at math). This is true even if the male/female gap is not genetic, since it's pretty clear that there is some sort of heritable component to math ability. Figuring out how this sort of thing affects performance could be very helpful, because even though it's partially innate (and somewhat based on brain chemistry), it can often be directly trained.
But if we declare by fiat that performance in math is primarily guided by factors outside the student's head (which is implicit in the "sexism keeps girls out of field X" argument), then we'll never figure out what's really going on, and we'll never discover how to help people that aren't predisposed to be good at math get better.