Yes, it's about good manners and politeness, and liking other people. I'd always give my seat to someone who needed it more. Rosesarered makes a good point, there have always been people who are only concerned about themselves. I do wonder how much impact on the way people communicate with each other in public spaces, the advent of parks with no parkie, buses with no conductor, tills with no shop assistant etc are having.
JessM - I think that's the problem with the word chivalry, it can be an excuse for misogyny. It's also part of the contribution to ensuring feminism is often seen in a negative manner.