Isn't it because planes are continually falling (because gravity), and this leads to two things:

1) wings increase the surface area pushing down (gravity) on the air below, which pushes back (air pressure), and

2) as wings are falling toward ground (gravity), they create vortices above the wing, which lowers the pressure, increasing the push up effect of the air below, and

at a certain speed, the vortices are stabilized into low pressure regions above the wings, and in a certain "envelope" region, of speed, plane shape, air pressure, all of these forces are equalized to give you level flight, so long as the dial you turn to get into the envelope region, "speed", keeps up.

That's how I understand it. Happy to hear a physicist / aerospace engineer guide me in how to think about this clearly.