I wonder if this is a US thing? Chivalry is well and truly dead here in the UK, just how I like it. The one time a man (my boss) rushed ahead of me to open the door for me I refused to go through it, lol. I'm an adult, I can get the door.

I think people confuse "holding the door open", btw. Of course anyone would do that for anyone, the "chivalrous" thing is going ahead to open the door for a woman and only go through after her.