I'd never dream of asking a guy to give up their seat for me based on the fact that I'm a woman alone. When the Titanic sunk, that was a different time with a different social etiquette. We live in a time period where we do strive for equal rights, where no life should be held at a higher value due to race, sex, religion, etc, etc...
In fact, I don't think many women would think that way. I don't understand all the "you asked for equal rights you got it now, *****!" going on in this thread. Women know that, and acting like the majority of us will try to bully you out of the way on that fact alone is well, wrong.
Besides, a true feminist would never suddenly state that their lives are more valuable than those of a man. They're fighting for equal ground, not superiority, and if they want superiority then guess what? They're not a true feminist.
Chivalry can go both ways. If I saw a father and his child I'd happily give my seat up for them so they didn't have to grow up without their father. However I wouldn't blame someone if they decided their own life was more important. We have a monkey-sphere, it's human nature to be somewhat selfish, especially when it comes to protecting our own wellbeing.
But seriously, if someone is standing behind you in line, hold the door open for them regardless of whether they're a man or a woman. It's rude not too, and you should expect the same common courtesy from them. Letting the door slam shut in someones face in the name of "Equal Rights!!1" is just rude.