In many physics textbooks, the explanation for lift on a flying airplane is that the top of a plane’s wing is longer than the bottom, and so air must travel faster across the top than the bottom, and therefore the pressure is lower above the wing than below. (This difference in pressure associated with different speeds of a moving fluid is described by Bernoulli’s principle.)
However, the problem with this explanation is that some planes nevertheless manage to fly upside-down! How could these planes fly both right-side up and upside-down? Could the top of the wing and the bottom of the wing each be shorter than the other depending on the plane’s orientation? This is absurd, and so there must be something wrong with the explanation.
For the correct explanation (briefly, the angle of attack of the wings provides overwhelmingly more lift than any lift produced because of asymmetry in the cross-section of the wing), check out the following references:
http://danielmiessler.com/blog/why-planes-fly-what-they-taught-you-in-school-was-wrong
http://en.wikipedia.org/wiki/Lift_(force)
(A version of this post first appeared at my other (now deleted) blog, and was transferred to this blog on 20 January 2021.)