Holding doors open are just manners. You don't want it banging on the face of the person coming next to you. Honestly, I do it for total strangers too..

I think many men go to extremes when dealing with women. As you rightly mentioned they believe that either women need to be protected, rather stifled or if someone comes across as too headstrong, just left to fight their own battles. Either they assume she doesn't need help or it is their way of teaching her a lesson..

You will never usually find a man behaving that way with another man.