I am sorry but I disagree. Air as a gas is a compressible fluid. You can compress air with your hand. I don't understand why this is hard to grasp.
Basically it comes down to what is "lift."
It is known winged planes can not fly in a vacuum.
Rather planes fly by some sort of reaction force between air molecules and the wing.
You seem to suggest the wing is pulled up from the top. How does that work? Do air molecules have little hooks that attach to the upper wing surface?
Obviously no.
So lift is just another name for the ordinary newtonian reaction force. It pushes from the bottom.
How is that possible? 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.