As others have pointed out, you can move yourself in space using compressed air. However, it is unacceptably inefficient. You wouldn't actually be able to appreciably accomplish any goals.
One of the most important measures of a fuel is Specific Impulse. Specific Impulse linearly related to exhaust velocity, and it will be easiest to talk in terms of exhaust velocity because its tangible. The space shuttle SRBs have an exhaust velocity around 2500m/s. LOX/LOH engines can get up to 4400m/s. Ion thrusters, known for their efficiency, get to 30,000m/s or faster.
Compressed air exiting at the speed of sound clocks in on the order of 300m/s. So it's 1/10th as efficient as the engines we use today. The limit for Nitrogen gas is around 730m/s, so you should expect your thrusters to produce on those ranges.
Of course, this gets worse, thanks to the tyrany of the rocket equation. Another key feature of space travel is the mass fraction -- this is how much of your mass is your payload, versus how much has to be fuel. The equation is $\Delta V = v_e\ln\frac{m_0}{m_f}$, where Ve is the exhaust velocity. A mission that requires some quantity of delta_V to accomplish requires a mass fraction to match. If you have 1/10th the effective velocity, you have to have a smaller mass fraction on the order of $e^{10} =22026$. If you've got engines closer to the theoretical maximum, you're going to be on the order of $e^4=42.598...$ or $e^5=148.413...$ worse mass fractions.
This means that to move any given payload via air pressure rather than chemical rockets, you need to have a rocket that's literally hundreds or thousands of times larger. That's why we don't see them used for large maneuvers.