Why is the wrong explanation of "air travels a longer distance and creates a lift" so popular?
Long story short is that both Newton's third law and the Bernoulli's effect are two different ways of explaining the same phenomena. Accurate equations have been written to explain both. Newton's third law, the air being forced down and forcing the airplane up, is actually the effect of lift though not the cause. The cause of lift is the change in pressure.

The falsehood that is taught is usually that the two little air particles actually meet up at the same point downstream at the trailing edge of the wing at the same time. This is completely false. In fact, if you were to actually track two air particles, one over the top, and one across the bottom, the one going over the top of the wing will probably arrive much sooner than the one on the bottom! [Even though the distance IS longer] It picks up that much speed. Also they don't actually really meetup again afterwards at all.

The real pivotal relation (which I learned in my Advanced Aerodynamics class at ERAU using John. D. Anderson's book Intro to Flight) is the Kutta-Joukowsky theorem. Taking the time to explain this to a Private Pilot student would probably be a waste of your time and theirs but I will sum it up here anyway to be fair to the question. I will assume incompressible flow because after about Mach .3&lt; it starts to get more complicated.

The Kutta-Joukowsky theorem takes the integral of velocity times the cosine of the incremental angle of the distance along the closed curve. This is a quantity called circulation. The lift equation is then formed as lift equals density (altitude basically) times velocity times circulation. So if you really want get in-depth here is an article from MIT that explains potential flow theory. 

What you will find is that the cause of lift is indeed directly related to Bernoulli's principle in that the change in pressure is what creates the lift. However it has nothing to do with particles meeting up at the trailing edge because they never really do meet up. This doesn't discount Newton's third law either: lift can be explained that way but it is the effect of lift, not the actual cause. And yes, like you mentioned, even a flat-plate for example can create lift when angled right in a wind tunnel.