So I told to my friend as I felt like it was just, embarrassing and I didn't like it.
She said oh yeah well obviously it's a power play. Really? Oh yes
So being a bit of an arse I did a little experiment 
I would say no after you! At the lift. Most went. Some did a couple of after you back and forth and went.
Some would not. Literally would not go in before me.
After you!
No after you!
I couldn't possibly!
It's really no trouble, after you!
Etc.
In the end I folded otherwise the lift would go!
Getting out once I tried it and a man I worked with who was a racist sexist arse. Said. I cannot get out before a lady. You must go first.
!
I mean it was only occasionally over a long period of time. Not like hammering it.
In the lift once I was looking at phone and in back corner. Got to bottom floor. Felt eyes on me. Continued deeply engrossed in phone. No one moved. Doors closed we went up again!
I mean what?
When I didn't play my part and was cheerfully insistently chivalrous back, or didn't behave as required and expected.
I'd say about 5% flatly refused to do the thing they were insisting I do.
Fascinating. Power play. Woman expected to play certain role.
Now I know doors are a long term feminists are ridiculous thing. And I know that not liking it is seen by most as trivial pointless making a fuss over nothing etc.
And often deliberately taken to mean holding door to pass to person behind you which everyone should do.
But anyway. I found my little experiment enlightening!