This is because the forces are acting on seperate objects, forces only cancel each other out if they are acting on the SAME object, so if I push a door, I'm applying a force on the door, that is the ONLY force on the door, there are no other external forces acting on the door to cancel out the force I am applying. Newtons first law shows that an object remains stationary or at constant velocity only if the net force ON the object is zero, this net force is the sum of the external forces ON the object. In this case the only force on the object is the force im exherting on it so the net force is not zero.
Hope this helped