I've done this for whoever was in the elevator with me, I don't see this as a gender based courtesy either. Both people in an elevator, or arriving at a doorway, should attempt to defer to the other. If it's then offered for you to go first, then accept it and go! It's like the courtesy grab for the check at a meal with a friend. Everyone should do this.
My spot seems to be by the buttons. Maybe because that is where the phone is but I'm always holding the door for people loaded down or with carts. Women will often just walk out, but I can't remember a guy not thanking me. Anyway, I agree . We should watch out for others.