Please show me a reference where it says a propellor pushes against the air.
Any such reference he cites, you could simply criticize as wrong and not sufficiently authoritative--just as you have done in the case of the article that initiates this thread. What is needed here is something more definitive, I expect .
So let's perform a thought experiment: turn on a fan; observe that the fan blows air in one direction, and sucks in air from the opposite direction. Then apply Newton's third law to the fact that the fan is transferring momentum to air molecules, so that those molecules are persuaded to move in a particular direction. The conclusion should be obvious.