You're totally right there must be supervision; it's just a matter of how the term is used.
"Supervised learning" for LLMs generally means the system sees a full response (eg from a human expert) as supervision.
Reinforcement learning is a much weaker signal: the system has the freedom to construct its own response / reasoning, and only gets feedback at the end whether it was correct. This is a much harder task, especially if you start with a weak model. RL training can potentially struggle in the dark for an exponentially long period before stumbling on any reward at all, which is why you'd often start with a supervised learning phase to at least get the model in the right neighborhood.
"Supervised learning" for LLMs generally means the system sees a full response (eg from a human expert) as supervision.
Reinforcement learning is a much weaker signal: the system has the freedom to construct its own response / reasoning, and only gets feedback at the end whether it was correct. This is a much harder task, especially if you start with a weak model. RL training can potentially struggle in the dark for an exponentially long period before stumbling on any reward at all, which is why you'd often start with a supervised learning phase to at least get the model in the right neighborhood.