"they move the air backwards"
The English word push, describes that action perfectly.
They "push the air backwards, true. But, the expelled air "pushing against" the stationary air, is not what makes them work. This whole line of discussion goes back to some people, not any real scientists you understand, in the days before spaceflight, saying that rockets would not work in space, becaue there is nothing for them to "push against". But since they do not rely on "pushing against" anything, although they certainly push their propellents out, they work just fine in space.