Why do rocket have fins?

The fins on a rocket are just there to create stability. As long as there are enough to provide a restoring force against a disturbance, it shouldn't matter. But ...

Enough means at least three, symetrically placed, with enough area so that when the rocket tips off of its path a little bit the fins provide aerodynamic force to put it straight again. If you only had two, a disturbance in the plane of the fins would not get corrected and the rocket would veer off course. With three, any tipping off of the flight path hits at least one of the fins in a way to correct the misalignment. Four works, too. Any more than that and you're just adding drag, which will shorten the flight.

Note well that the key parameter is the area of the fin times the distance it's lift center is behind the mass center of the rocket. That's why something with the fins behind the engine nozzle works so well, because the lift center is behind the entire rocket. Before I knew that rule I built a seriously overpowered rocket with gigantic fins that came all the way up to the nose. Instead of flying with great stability as I expected, it jumped off the launch rod and headed for launch control, then writhed on the ground like a beached whale until the parachute charge went off.