Chivalry and Sexism - Directly Related?

There seems to be far less chivalry today than only 50 years ago. Men don't often pull the seat out for women. The first person to leave the elevator is usually who's ever closest.

There's also far less sexism in the world than 50 years ago.

Do you think the two forces are directly related? The more sexism there was, the more we did to give the impression that women were respected and powerful. With less sexism, we needn't invent such masks.