tl;dr: Codidact is contracted from "co" (together; Latin) and "didact" (to learn; Greek)
There has been a forum discussion for that question, too, I'm summarizing the important aspects from there:
That’s because the Co- is one part (Co=together, could be short for “Community”) and the -didact is another part (didact=teaching).
If I recall correctly, the story behind it was, that some user wrote that they are an autodidact. That lead @rodolphito to suggesting it. In a majority vote we decided to use it as our name.
co for together and didact for learning.
Both co- for “joint”, “communal”, “shared” and -didact for “teaching”, “learning” are very common. One comes from Latin, the other from Greek and they’re both used very widely in many, many languages. Think of words like cooperation, didactic, combined, autodidact,… Codidact immediately suggests things like “teaching each other” or “learning together”. Just like autodidact means “self-taught”.