I'm confused by this, humans already had well-developed and complex language well before we started moving out of Africa into Europe.

Relatively high divergence of language across a relatively small geographic area? How often, exactly, are you interacting with people outside your family group? Outside your local group of family groups? Even factoring in nomadism.

> a time when humans could barely speak with eachother.

That's a pretty wild claim

We don’t know anything about Neanderthal language, or even whether they had something we would consider language.

We’re talking about the Homo sapiens here since they would be doing the enslaving.