Then what could possibly be the cause of a biological innate gender identity?
Although the whole genome has been mapped, scientists don't yet fully know what it all does or can do. I think the last estimates I read were that they had a fair idea of what 20% does but that 20% might have impacts that they don't understand.
Do you take this as evidence of gender being a social construct?
I don't think that we can take any specific piece of evidence of behaviour or attitude as being proof of anything. I can throw out a good few women who ruled Egypt, Wales, England, Acient Greece, etc. who obviously overcame those beliefs but neither piece of information negates the other.
I occasionally find myself doing a weird bit of gender performance, and I have no idea if I'm doing it because I'm female or because I'm a woman, if it's cultural, a habit or just me. If anyone else can break this sort of thing down, I'd be delighted to hear what they have to say.
I'm not claiming to have all the answers, I'm just pointing out that some people are stating a theory, for which there is no definitive evidence, as fact. If the starting point in a discussion is that one groups has the 'facts' the discussion doesn't go very far.