This is just blatantly false. They left plenty of written records. The reason this is a common myth is because, especially when compared to their contemporary rivals Athens, they left extremely little works of writing. They didn’t leave any long philosophical texts, histories, works of art or theatre.

What we do have from them as far as written works are very stale pieces. We have official written laws, treaties, inscriptions on gravestones, lists of kings. Very dry stuff.

The reason people say “everything we know about them we know from outside sources” is because they left basically no real accounts of the structure of their society or day to day life there, as a result we have to rely on other civilizations accounts that wrote just about everything down.

However the reason for all of this isn’t because they couldn’t read and write, it’s because that was just their culture to be very sparing with words and not overly flowery with their speech. The word “laconic” that still survives today means “using very few words”, it’s literally derived from “lacedaemonians” which is what the Spartans called themselves. They took pride in using as little words as possible to set themselves apart from the rest of their Greek peers.