Chivalry is weird.
I have a theory.
Let’s say you’re walking down a flight of stairs that ends at a landing leading to a door. As you descend, you hear footsteps above you also leading down. It turns out it’s the nice lady you smile at at work. You don’t know her. You just smile. By the time you reach the lower landing, she’s at the landing above where you were 13 stairs ago. Do you (a) open the door and walk through it to lunch (b) open the door and hold it for the nice lady behind you. (c) it depends.
Let’s say you chose c based on a relative feeling of how far she is truly. What if you mess up? What if you choose to hold open the door when really she’s just too far away for you to be doing that? Now she has to hurry down a flight of stairs, putting herself in more danger considering her heels, to oblige the grinning fool who insisted on opening a door for her that she could have easily handled in her own time. I dread this. I would hate to have her slip and fall on my account of “chivalry”. Instead, barring an extremely close encounter, I choose a. Not because I’m not chivalrous, but because I care enough to have thought about it. I care enough to not make her change her walking or climbing pace or pattern if she doesn’t want to. Therefore, I continue down the stairs, open the door and whistle merrily to lunch knowing that my passive act of non-chivalry probably did more good than what’s traditionally expected.

Another scenario. It’s a really cold day in one of the ten months of Michigan winter.
You and your friend that’s a girl are running out to the car having just eaten good Korean food in Ann Arbor. As you approach the car, you could (a) run around to the driver’s side, turn on the car and blast the heat (b) open the passenger side door, make sure she gets in ok paying close attention not to catch her scarf in the seal, then run around to the driver’s side, get in and blast the heat.
To me, this one’s a no brainer. If you half way care about this person, or any person that rides with you in Michigan winters, you get in that freakin’ car and you turn on that freakin’ heat. Right. Now. None of this, “Oh, are you okay?” “Watch your feet!”
Naw. Any time wasted before turning on the heat is cruel punishment for having an uncaring friend. It’s not that I don’t care. It’s that I care so much, I’m willing to sacrifice what you think of me.