Your description is incorrect for several reasons. First, the "typical airfoil" is not flat on the bottom, but whether it is flat or not isn't really important to understanding how an airfoil works. While some airfoils are indeed flat bottomed, most are assymetrical. Some are even completely symmetrical. I won't explain how a symmetrical airfoil works, but it's a good brain-teaser of a question.
Second, there is not less friction on the upper surface of the wing. The air flowing over the top of the wing is accelerated due to the shape of the airfoil and angle of attack (in other words, the air has to travel further in an equal amount of time as air flowing beneath the airfoil), creating lower air pressure above the wing than below it. This is explained by Bernoulli's Law of fluid dynamics (look it up). High pressure is not "created" on the underside, relatively lower pressure is created on the upper side, and the differential creats "lift". This low pressure area above the wing does just as much pulling (or sucking is perhaps more descriptive) as the "pushing" caused by the relatively higher pressure air flowing across the bottom.
Corporate pilot (ex-airline), Flight Instructor, BS degree in Aeronautics.