A wing holds a plane up by throwing air downward
Stick your hand out of a car window and tilt it up slightly. The air gets deflected down off your palm, and your hand gets pushed up. A wing does the same, harder, with a curved top surface that bends the passing air downward too. Push air down, the air pushes you up. The school story that air splits at the front and must meet again at the back is simply wrong, and it is not why wings work.