N.B. Bookworm, Engineers and Scientists are most certainly not sure about why wings fly. We are pretty confident that we can predict whether they will and how well, but as to why - no. I asked this in my office (containing four qualified aeronautical Engineers from CEng to HNC) recently and nobody was prepared to say that they did.
Oh c'mon Genghis...
That's tautologous. By that standard no one can ever say "why" anything in nature is the way it is, we can only explain it in a quantitative and predictive way in terms of other models.
If you see an apple fall to the ground, can you say "why" it fell? You can certainly predict whether it will and how fast, but "why"? That would seem to require the mind of God.
Low-speed aerodynamics is as well understood as any other area of applied physics, and to maintain that science has been baffled for 100 years by the nature of lift is simply daft!