ONLY if the door is heavy, a man enters FIRST, while pushing it open and holding it for HER to enter behind him. He may enter a revolving door FIRST to get it started, but lets HER first if it is already moving.
It is simply basic good manner for a man to open a closed door for a woman. That includes car doors…before he jumps in ready to go, even if he is a passenger..
When the door of an elevator opens, women enter before men and exit before them. Except if the elevator is full of people in which case the closest person to the open door exits first. He may also push the buttons to indicate floors. Brief, he should ALWAYS let her go through an open door ahead of him.
Younger men can be assured the despite today’s equality between men and women socially, this is the right way to do and if a woman does not approve, she is just unaware of the rules of social etiquettes.
WOMEN TOO need to hold doors when someone is holding a lot of packages, pushing stroller or in a wheelchair.
However when in Japan do as Japanese do….. Women maybe expected to let men go first…
Last but not least, holding the door for someone behind you, of any gender, is simply basic manners.