Good paper, but there is a good amount of evidence that gender is not just a social construct, but there is a biological basis for it.

I've read various things about it, and it just seems that the stereotypes that have evolved didn't just arise from thin air, but have come out of differences between the male and the female that are just there. I've read of communes where they treated the children all the same, no gender-specific behaviors pushed, no talk of what the girls shouldn't do because only boys did, and so on. Guess what? All that effort, and they still found the children doing it on their own, the boys mostly playing in one manner, the girls in another.

For an strong example to demonstrate the innate gender identity that a person holds, examine the case of David Reimer.

Sure, there are a ton of purely social and cultural things still around. But the two are different in many ways, and that can't be avoided. I don't think everyone will fit into one category or another, because there's always variety in nature, and occasionally there wil be people who break the rules. But only occasionally.