I have a modest proposal on a source of divergence of natural languages. There is a common notion that we humans identify with groups and need and want to indicate to others which group we belong to. I suggest that idioms arise partly due to this influence. Some idioms arise despite well known older idioms which mean virtually the same thing, except for what they say about the speaker. In tribal times there seems to have been issues of tribal loyalty whose flip side was suspicion of members of other tribes. The few examples of dialects in close contact with each other that I have first hand knowledge of, are accompanied with at least occasional conflict, if not violence.
Of course there are other probably more significant sources of language diversity. Any sort of language drift or new subject matter produces divergence when the speakers seldom come into contact with each other. Dialect variation in high density population centers can not be easily explained this way however. Some sorts of memes leak across language barriers without bringing the associated words along.