Why not? Look at it from the bottom up:
Communication is a fundament of life, from intra-cellular to inter-cellular to inter-organism interactions (another fundament is the ability to keep oneself in a low entropy state, at the expense of the rest of the world).
Human speech is an evolution of mammal communication. It grew up in complexity, from grunts and other basic noises, along with our way of living, up to what we have now.
> And how do we make completely novel utterances that attempt to express our otherwise abstract thoughts?
Speech is a big collage. New is either the result of
* a recombination of the sub-parts of past speech
* the definition of a new word in terms of older words, or sometimes arbitrarily (for proper nouns).
Nothing fancy AFAICT.