Planes and rockets fly using different principles.
Planes take advantage of aerodynamics, they use wings that create lift when air moves over them. This allows a plane to fly without needing to use a tremendous amount of force to counter gravity. You only need thrust to push the aircraft forward fast enough to generate lift.
Rockets meanwhile are purely brute force. Chemical propellants create thrust to counter gravity and accelerate them into space. Rockets need to do this because there is no air in space to generate lift, and having wings at some point actually only creates drag and slows the rocket down.
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