Why is it necessary to cool a hot supersaturated solution slowly during a recrystallization?

The answer is; it grows large crystals.

The reason we dissolve a solute in a hot solvent is so as to ensure more solute is dissolved hence making the solution supersaturated as it cools down. Slowly cooling the solution allows the molecules to align themselves into crystal lattices (regularly arranged molecules) as they come out of the solvent intermolecular spaces (because the cooler the solution becomes the less the solute it is able to dissolve).