I have a tentalizing scenario for the whole "holding the door" conundrum: double doors. Walk into a restaurant, mall, or building with double doors, whoever gets to walk through the first door held open for them is going to reach the second door before the other. And there comes the "test", (1) will the person return the favor (and establish equality of manners), (2) will the person slow down expecting the gallantry to be repeated, (3) will the second person rush in to hold the second door too, or (4) will the person just open the door and walk through (and probably holding it open for the second person).
To me, the first case is nice and pleasant for all parties involved, even among strangers, it just feels good to care for others and/or be cared for. The second case, which would usually involve a woman as the person waiting for the gesture of gallantry, is a bit backwards and weird, and I don't think anyone (of my generation) likes that, whether on the receiving or giving end. I think few men are still attracted (if ever) to the whole "I'm a princess and you're my knight" thing. And if women are offended to be put in that role, then great! The third case is also bad for the same reason, except that, in that case, the man is trying to put the woman into that princess/knight paradigm. In the last case, clearly the person doesn't care much about the gesture of courtesy, which is also OK, as long as minimal courtesy is still there.
That's the way I see things, but I certainly would like to see more of the first case, i.e., people being happy to take a little pause or sidestep in their day to care for others with simple gestures like that. If you give, you don't feel bad or uncomfortable about receiving.
By being chivarlous a man suggests he admires/agrees with those times and opinions
I associate the word chivalry to that princess / knight paradigm, or the Guinevere / Lancelot type stories and fairy tales. It used to be the ideal of romance. But that's changing because I think people see it as an unequal relationship, and in both directions. Modern women aren't comfortable in that passive "marry rich" role, and men aren't comfortable with that either, both want a real partnership these days, and that's a good thing. And gallantry gestures are just one of the subtle (or not so subtle) ways of sending a message like "hey, I want to be your knight", and you can't expect most women to like that very much, unless they make it clear that they do.
Do I hold a door open for a woman because I want to have sex with her?
Ishh... sometimes I get the feeling that women think men are like lap dogs, they just want to hump everything they see. Not that it's completely unjustified to think so, but give us a break!
chivalry is based on the view that women are frail, fragile, weak, and should be treated by men like a crystal vase.
Well, one problem with that is that women are weaker, i.e., smaller in stature and with weaker muscles in general. At my university many of the doors are quite heavy, and I often find myself opening the door for women not because of "gallantry", but just because they are often struggling to get them open and since I'm 6'2'', I can just extend my arm and open the door with no effort at all. But there is a big difference between that and ascribing a prejudice of weakness or fragility.