As I said I have girls. I teach them to hold the door for someone coming in behind them. I teach them to give up their seats (well at least my 10 year old; I just have my 6 year old sit on my lap) to older people, pregnant women and a parent holding an infant.
It's polite and it's good manners, IMHO.
But when a man holds a door for a woman and lets her enter first or pulls the seat out for her at a restaurant, or helps her with her coat, or gives her a seat because she's the only woman standing, I find it refreshing and nice to see that chivalry isn't dead and gentlemen still exist.
If that's sexist then I guess I'm sexist too. Luckily, I found a DH who feels the same as I do and who was raised a gentleman.