Why does cold brew take hours to make when hot coffee brews in minutes?

Answer: Because cold water extracts flavor from the grounds more slowly.

Because the coffee grounds need time to ferment in the water. — Not quite. Fermentation can happen during coffee processing before the beans are roasted, so the idea is not random. But in cold brew the water is extracting already roasted grounds; the slow step is low-temperature extraction, not the grounds fermenting in the jar. The long soak does not need fermentation to work.

Because cold water extracts flavor from the grounds more slowly. ✓ — Right. Hot water gives the water molecules more energy, so soluble flavor compounds leave the grounds quickly. Cold water extracts them much more slowly, which is why cold brew makes up for low heat with a long soak. The long time is about extraction speed, not fermentation or caffeine alone.

Because caffeine dissolves more slowly than the other flavor compounds. — Not quite. Caffeine does dissolve into the water, and it is one of the compounds extraction pulls from the grounds. But cold brew's long time is not explained by caffeine alone; many flavor and aroma compounds also move slowly at low temperature. The hours are for the whole extraction, not just caffeine dissolving more slowly.