[rawgabbit]

You cannot compress air with your hand. What you are doing is displacing it, moving it somewhere else.

What you described It is possible because there are more air molecules colliding with the bottom of the wing than with the top. I.e. pressure is higher beneath than above. These collisions transfer kinetic energy from the compressed air to the wing. -- when I was in school a long long time ago -- we called it LIFT.

We called it lift because at subsonic speeds, airplanes relied on Bernoulli's principle. At supersonic speeds, the shock wave created at the bow of the wing prevented laminar airflow meaning no LIFT. At supersonic speeds, the airplane flew due to the newtonian breakdown of airflow against the wing's undersurface. At supersonic speeds, airplanes are inherently unstable which meant they relied on computers to constantly correct their trajectory.