So I murdered chivalry

Awhile back I had a philosophy class that didn't have enough seats on the first day. Twenty minutes into the class a boy with buzzed hair and a striped polo raised his hand. "Oh no, I didn't have a question about the syllabus," he said to the teacher and turned to the girl sitting on the floor, "I was just wondering if you wanted my seat."
She awkwardly shook her head and our teacher exclaimed, "Chivalry is not dead!"

These kinds of things make me want to conduct an experiment-- start opening doors for boys, giving them my seat on the bus, and throwing my coat on puddles for them. I could document the reactions. (Starting Monday, maybe I will start subtly integrating reverse-chivalry into my routine.)

Should I have felt relief that the guy in my philosophy class was looking out for the girl or should I be annoyed that he interrupted class because he didn't know if a girl could sit with all the other boys on the floor? She wasn't wearing crutches or anything, she was just a pretty blond. Should she have felt flattered? Should society commend or condemn this behavior?

There are ways to be respectful that aren't so deeply rooted in Christian traditions and make more sense. There are ways to be respectful that don't assume gender roles. We should replace chivalry with something that goes both ways, men and women should be held to an equal standard. I can open doors, I can sit where boys sit, I can stand on a bus. Unless I'm expected to do the same for another girl or for a guy (like help with a heavy load), then why should men do it for me? If a girl makes more money than her boyfriend should she expect him to pay for every dinner? I just don't feel that the only alternative to chivalry is disrespect or that the two are mutually exclusive.

Unfortunately, there are many who disagree. They are misty-eyed about the days of knights and I've even heard people refer to it as a time when people married for love, not money. Fortunately, these kinds of claims can and do earn the response I'm looking for. I feel like this nostalgia ignores and confuses historical facts, women benefited from chivalry because it was meant to help the weak. I don't intend to be weak so I don't know why I should desire to be treated as such. So instead of trying to act like people in the Dark Ages, why don't we try to act like people in the 21st century?

Now my question is how are men and women supposed to treat each other in a post-feminist society? The answer is simple reciprocity. Just treat me as an equal and don't assume strict gender roles, I'll manage carrying my own books, standing on busses, opening doors, voting, and going to work whether or not a guy can respect that. I'm not mad when others try to do those things for me, but I like, no, LOVE when they think through all of this and stop assuming they know what's good for me, that I might be more thankful when a guy respects my independence and lets me take him out from time to time.