I have to agree that there is no reason to give up your seat just because there is a woman without a seat (pregnant, holding sleeping baby, elderly, infirm, sure, but just because they are a woman, no way). Sorry, but to me that seems too much like "oh, yes, we must let the little lady have a seat".
Let me add, before everyone jumps all over me for being a chauvinistic male, that I am a woman who is over 50 (and fast approaching 60

).
And while I do think that chivalry is dead (or at least on life support), people should be aware of the attitude and lack of response that they may be giving. Let someone in front of you in traffic and don't even get so much as a wave in thanks. Hold the door for someone and get no comment. Give someone your seat and not even get a nod. Yes, they have all happened to me recently.