The shape of the wings is not the whole story. If it was all due to the shape of the wings then planes would have great difficulty flying upside down!
Military aircraft with flat wings still manage to fly, and this is due to the Angle of Attack, the orientation of the wings Chord to the airflow. Try it yourself, in a moving car stick your hand oput the window so that the palm of your hand is facing and parallel to the ground. Now rotate your wrist so that the front edge of your hand tilts up. You will notice it is now keen to move upwards!
Look up the Coanda effect as well as this is also relevent to wing design.