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Why isn't pressure used as flight?

I've heard that 2L bottles can hold a pressure of up to 90 PSI safely. Since $F = PA$, if the nozzle of a pressure rocket is about 4 inches squared in area, that would be a thrust of 360 pounds!? Is there something wrong with my math, or why don't we just pressurize air and use it for flight?

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The principal disadvantage is the indirect use of energy. Energy is used to compress air, which in turn provides the energy to run the rocket. Any conversion of energy between forms results in loss. Hence it's more economically efficient to burn fuel rather than compress gas and then release it. This idea has been used in Compressed Air Cars much before. Also look at Compressed Air Energy.

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In a way it is. A jet engine will create a high pressure region in the combustion chamber and discharge it through the nozzle. It turns out this is inefficient, and it is better to use the pressure to drive turbine blades that push the cold air around the engine. Remember cold = higher density = higher momentum.

To a lesser degree a propeller will create a high pressure region behind the blades, that results in thrust.

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