I like the idea proposed by I think Larry Niven the SF author, that speech started as a way to bypass and augment the corpus callosum so the two hemispheres of the brain could get more in sync, and provide a way of organizing, "do this, then do that, then 'be careful here' swing the rock and release."

Think about the internal focus you have when doing something carefully and how you talk yourself through it, from carpentry to skiing.

Using the same verbalizations, when showing someone else the same thing, evolves to language.