Holding the door for someone is just plain courteous. If I am the first to arrive at the door, I hold it for anyone else wanting to come in.
(So long as it is a not a non-ending line.) I expect, and usually get, the same courtesy - whether it is a man, woman, or child who first opens the door. As a 62-year-old woman, I am delighted when someone offers me assistance; I don't usually need it, but I don't dis it either.