Your argument sounds nice, but does not offer sufficient proof for your rather strong statement "so the natural biological differences are irrelevant". This is

Your argument sounds nice, but does not offer sufficient proof for your rather strong statement "so the natural biological differences are irrelevant". This is a claim which could be scientifically tested. For example researchers could develop two rudimentary tool chains, one for women and one for men. Then they could investigate if in fact they can generate any statistical difference in participation. It would actually be a rather interesting theory to test, and I would hope someone does test the theory. However your claim is not currently known to be true, rather just a promising theory.