Along with countless others I was taught that it was all down to Bernoulli and his theory of a faster flow over the top of the wing. I realise now that it's probably not the case but I still find myself teaching it, and glossing over what I know to be an elephant in the classroom. To proffer anything else would have done far more than raise the eyebrows of any trapper during a CFS check all those years ago.
The flat plate theory - or a streamlined one - does make a lot more sense, and when explained along the lines of sticking ones hand out of a car window makes it easy to visualize that when lift is generated, so too is drag. It's also pretty easy to prove that symmetrical airfoils work very well indeed - just look at any of the advanced aerobatic types in production.