I think I get it — but I don’t want to presume.
As a dad of two adult daughters I have been outraged over what they (and my wife) endure. But not every act of kindness is intended in a sexist way. From my own perspective I don’t find it awkward to have a woman open doors for me. And in a similar scenario, if the person were a male, I might have done the same for him: “wait, let me get that for you”.
All the same, many times what you experience is typical. If you were a guy he wouldn’t have insisted — that can be bothersome and demeaning. There are centuries of sexist behavior that just cannot be ignored: they form the context in which we swim and sometimes we (men) just act out those contexts without thinking. Sexism can be an automatic response as seen in the demand that you allow the door to be opened for you.
I wish to honor your point of view as valid. And I feel very awkward in giving a counter-point (because you are right…it’s not about the stupid door). Too, I acknowledge sometimes my daughters shake their heads and say, “Dad, you’re missing the point.”
I’m willing to concede that may be the case. So please forgive me if I’ve totally missed it. (And I won’t mind the correction). 8^)
Call it my southern upbringing that one always open doors for people when they have the opportunity regardless of their gender. Thank you for your perspective.