writes:

The point is that any theory that says an aircraft flys by forcing
air downward fails to explain how gyrocopters and gyroplanes fly.

No, it doesn't. The rotor of the gyrocopter is essentially a large airfoil
(in addition to being a set of small rotating airfoils).

Airplanes, helicopters, gyrocopters, and gyroplanes all fly in
level flight due to the lift produced by the wings and/or rotor blades.

And that lift is produced by accelerating a mass of air downwards. There
isn't any other way to fly (except via direct thrust from an engine pointing
downwards, as in a rocket).