Why doesn't the pressure inside an airliner push the doors open?
Most of the airline doors are plug type- i.e. they are wedge shaped, so that the pressure differential pushes it against the fuselage and prevents opening. For example, the following image shows the Boeing 737 door.



Image from airteamimages.com

Note that the door is bigger on the inside, so that when it is locked in position, the pressure will push it against the fusealge, preventing it from opening. For opening the door, it has to be swung inwards before moving out.