[marvin]

For upside-down flight, though, the shape of the wing isn't irrelevant. Many aerobatic aircraft have symmetric wing profiles, since the curvature of the wing reduces performance when inverted. (Higher speeds are required to maintain the required lifting force, and drag is increased).

Some of the popular explanations of aerodynamic lift are outright wrong, but most of them are correct about part of the story. Our CFD equations are obviously correct, otherwise our simulation software would give bad results. Maybe it's just hard to explain the results of these equations in an unambiguous way.

It is true that "air goes down, wing goes up", but this explanation is only one "why" closer to the heart of the matter.