What's funny, is the automatic assumption that a man has to give up a seat.
I was on the NYC train one time and a lady asked me to have her seat because shes a woman. She made some comment about chivalry being dead. I politely declined and she wasn't happy.
The reason I declined was because I was born with bilateral club feet and have had like 4-5 surgeries on my foot, and as a result, I have bad arthritis in my feet. I can't walk or run for long periods of time and that day my foot was hurting bad, so I needed to sit. She just assumed that I was being an inconsiderate male without realizing the real reason why I wouldn't give up my seat. Yet, in her eyes, I was just a selfish, inconsiderate guy. Not to mention, she was young, like in her 40's. If it was an elderly woman, I would have grin and beared the pain. But, not for her.