Finally, air can have kinetic energy, as any windmill owner will tell you. Now it should be getting obvious. A bunch of air moves across a wing. Since you can't spontaneously create air, the amount of air that enters the front of the wing must also leave the rear of the wing. Clearly in order for this to happen, it must move faster over the top curved surface than over the bottom flat surface, after all, it has further to go.
Energy is conserved, so the pressure energy plus the kinetic energy stays constant.
Now on the top of the wing, the air is moving faster, so it has more kinetic energy, therefore it must have less pressure energy, and so the plane flies. That is also exactly how a sailboat is able to sail against the wind. One mystery solved. The next mystery occurs when the wind is more or less at right angles to the boat as in Fig 4. As every wind surfer knows, this is where you really want to be.