Step-by-step explanation:
Neon is in group 8/0, which means that it has a full outer shell. Atoms react to get a full outer shell but as neon already has a full outer shell, it doesn't react and stays monatomic.
However, chlorine is in group 7, so it needs 1 more electron to complete its outer shell, two chlorine atom share one electron each with each other so they have full outer shells. This is why chlorine is diatomic.