How can air rocket generate thrust with out having any air to push against in outer space?

This is due to Newtons 3rd law of motion:

"When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body".

The first body is the Rocket, the second (as it has mass) is the air blowing out & away from the rocket .

Look at this way, if you (representing the air) are standing on a skateboard (representing the rocket) and you run off the back (without touching the ground), then the board rolls forward as you go backwards.

It does not need you to touch the ground (like the air to push against anything) for this to happen.