And yet you have no mechanism for water to push off air.

Prove that there is no mechanism

No, YOU prove that rockets need air pressure to provide thrust when the simple application of

*conservation of momentum* shows that they need none!

Rockets need no air to "push off" because most of their thrust is due to the rate of change of momentum of the exhaust gases.

There are numerous references to the derivation of this but I'm still looking for a simply presented one but they all end up as:

The source of that, at

Rocket Thrust Equation, gives more details of the significance of the various terms.

Now that might come from NASA but they did not originate it.

The design of some rockets with their combustion chamber, choked De Laval's Nozzle and divergent bell date back to at least the work of Robert H. Goddard,

Robert Goddard and His Rockets and almost the same in

Robert Goddard: American Father of RocketryThere is more discussion of the rocket thrust equation in

ROCKET PROPULSION, Supplement #1, Rocket Nozzle Design: Optimizing Expansion for Maximum Thrust.

So, deny what you like but, not only do rockets need no air pressure but they provide more thrust in a vacuum that at sea-level.