Nor do we know how airplanes work. Or whips.
There maybe a few gaps (particularly for supersonic flight) still being explored, but in general it's inaccurate to claim that we don't know how airplanes work.
The speed explanation is not incorrect, except the REASON for it is.
I learned on school that the air on top of the wing move faster to catch up with the one in the bottom (this never made sense to me...), the air on top indeed move faster, we only don't know why.
Damnit, I should be a physicist, not a programmer :P
* BLAS (please)
* LAPACK
* memset
* memcpy
* 'Segmentation Fault' is not a synonym for 'exited successfully'.
Next, you'll tell me that 'Thank you for playing Wing Commander' is not a synonym for 'EMM386 exception 006A at 00B8:3128'.
We know exactly why. The mass of air above the wing is moving into a larger physical volume, so it spreads out to a lower pressure. Bernoulli showed that pressure and flow velocity are always related (for non viscous flows), so where you get a low pressure you'll also get increased velocity.
The "to catch up" part is wrong, as well as the idea that it's the "longer path" that makes the air speed up. A symmetrical airfoil still generates lift as long as it has some angle of attack.
Now, there is one complexity here in that air isn't totally inviscid. It does have some viscosity, and this creates some complex boundary layer effects and turbulence. So the Bernoulli explanation is a bit of an approximation. The "real" math is Navier-Stokes, but that's not useful to most people for understanding flows based on looking at formulas (it's the math that underlies computational simulation of fluids but nearly useless with pen and paper).
A better "highschool textbook" explanation is the concept of circulation, which captures most of the important details without requiring you to understand tensors and vector calc.