[AndrewSwift]

You can see why planes stay in the air by sticking your hand out a car window.

If you know better contradict me, but:

An inclined flat surface will push air down, creating pressure below, and create an empty area above, creating a partial vacuum pulling up.

Airfoils are used instead of flat surfaces because they eliminate turbulence by creating laminar airflow.

Regular planes are not built for flying upside down and have airfoils optimized for regular flight — the airfoil section we're all familiar with.

At an airshow once, a pilot showed me that on a plane built for acrobatics, the wing section is vertically symmetrical.