I really don't think it's sexist. I hold doors open for people and I greatly appreciate it when people (man or woman) hold the door open for me. People just want to look for things to complain about and think every little thing that men do is sexist.
I respect your point of view. But I disagree. I think that holding the door open, or offering a woman a coat, or even refusing the split a bill is a form of sexism. I don't doubt that this comes from a well-meaning place, and that all the man wants to do is be kind. What bothers me is that subconsciously this comes from the idea the men are strong and women need to be protected and taken care of. It just enforces those stereotypes. It is a nice gesture, though.
It is a nice gesture, though.