Many things, personal experience in things like athletics competitions that I used to do in elementary school. It certainly wasn't a sausage fest, plenty of competitive girls were involved albeit in different activities compared to the boys, generally speaking. I didn't see any discouragement on behalf of my gym teachers towards the ladies, they just seemed to prefer certain kinds of competitions.
I've noticed something and it has held true for me: women both do better in and gravitate towards cooperative team-based competition as opposed to men who seem to like solo competition or hierarchical team-based competition where you either lead or fall in line.
It also seems to be the case that the more gender egalitarian the society is, the more the biological differences between men and women exhibit themselves, much to the dismay of certain people it would seem who were hoping for more parity.
The degree to which people want women to be like men almost seems like an admission that women are inferior or something. Why is it just assumed that women should be doing as good as men in something like chess? What is this assumption actually based on?