I open doors for men and women. I open them for the elderly and children. The different sexes seem to take it differently, so to men I do it in a way that is like, "Well, I was here, so I may as well hold it open."
But I agree with #37. Benevolent sexism is a stupid idea. I see things all the time where women say they think a gentleman should open the door for them and do other such things.
Maybe I'll get bashed for this, but even if there is no real inequality, there will be some things that are different between men and in women when taken as an aggregate because people in general like them that way or because men and women, on average, make different choices. I don't think there is a way to make things equal in a way that will make everyone satisfied.