If you’re asking about the etymology of idiolect:
idio-: from Greek idios “particular, individual”. Cf. idiosyncrasy, idiot (originally: private citizen, loner), idiom.
-lect: back-formation from dia-lect, originally “something conversed about/in”, from dia “through” and lektos “spoken”.
If you’re asking why there are idiolects, where they come from:
We like to abstract languages, sociolects, and dialects as the common property of a language community. But that is always an abstraction.
What occurs in reality is that each individual has their own mental model of a language, with their own influences from the people they’ve learned from and spoken to, and with their own individual variations.
Idiolects are the source of all language variation and change: those variations are levelled and grouped together because people talk to each other, and that’s how the higher groupings of languages, sociolects, and dialects are real.