I enjoyed your explanation but I still have an argument with the statement above (not yours). It implies the force is derived from "pushing" against the air which is a popular misconception and totally ignores the fact that the air or water is accelerated by the propellor.
Ah. I see. I interpreted that statement as simply referring to the fact that the propellor blades transfer momentum to molecules of air by hitting them, although I admit that "push" is probably not the best verb to describe the process.
It makes sense if you think of the necessity to "push" on the air to expel it rearward at a high velocity, imparting to it the necessary momentum, which is also increased in the forward velocity of the propellor.