There is a lot of confusion about holding doors. In social situations, a gentleman opens and holds the door for a lady. But in the business world, business etiquette is gender neutral, so the one who reaches the door first - man or woman - opens and holds the door.
If you are going through the door and there is someone right behind you, pause, so the door does not swing back and flatten his or her nose. If someone holds the door for you - man or woman - the proper response is, "Thank you." If you open the door for someone and the person barks at you, "I can open the door MYSELF!" Do not be a "door boor"- do not respond with a personal attack and do not defend yourself. ("That's the way I was taught!") Simply smile and go about your way.
This etiquette tip is provided by the Culture and Manners Institute at http://www.cultureandmanners.com/.