You step out into the lobby. Therefore, the closer you are to the pivot, the more force you must exert to apply the same amount of torque. As you push on the door, it begins to turn more and more quickly. By applying torque, you are giving the door angular impulse, which transfers angular momentum to the door and makes it accelerate. The door tends to keep on turning after you stop pushing, and it can bump you if you re not careful.
Angular momentum keeps it moving.