Chivalry, at its core is definitely sexism. It is treating someone different because of their gender. You can see it in one of two ways.
1) female supremacy. Treating women better because of the sheer fact that they are women. It implies that all women are better than men, no matter what.
2) You could also see it as against women, implying that women need men to do everything for them and that women cannot be independent. This is inequality. Chivalry is not dead, but it should be.
People really need to look up Chivalry:
Chivalry is an ancient guideline of conduct, used by Nobleman, Knights, its not about one gender being better than the other, this is an idea that began in the 11th century, some of the things in the code are no longer politically correct, due to the code eventually getting altered during the time of the crusades.
The Modern Remnants of the Code/(Guidelines since no one forces/d you to use Chivalry) of Chivalry that are still used today are the use of basic manners, courteous behavior, esp towards women and put simply not acting like an idiot around people in public.
Chivalry is an old concept most of it is no longer relevant to everyday life. Although the Quality's of Knighthood part of Chivalry are still relevant within the Modern Military/Police/Emergency services: esp courage, honour, justice, and a readiness to help the weak.
And since Woman also do those roles why can't they be Chivalrous? Who says a man or a woman can't come to the rescue? Does it really matter which, so long as your saved when your in real trouble?
Chivalry is a number of different ideas and concepts of how to be a good and honorably person by past centuries standards.
There are Three main types that frequently overlap some of the same basic concepts but each is slightly different:
I see no reason why women shouldnt expect both equality and chivalry, the two are not mutually exclusive, chivalry is merely a way of expressing respect for women with common courtesy and a polite behaviour pattern, its not bowing to womans superior will, nor is it meant as a means of insulting their capablities, its simply a matter of manners
Men don't open doors or tuck in our chairs because they think women are unable to, but because it is a sign of respect. And I am pretty sure that neither I nor the man think that he is doing this because women are superior. Honestly some people need to calm down and not criticize people for trying to be a decent human being.