From a Darwinian perspective, the presence of a particular trait in a species must be explained in terms of the evolutionary advantage that specific trait conferred upon that species. That is to say, possession of that characteristic would make that species more fit and thus more likely, through the process of natural selection, to survive over time. Consequently, a Darwinian explanation of the origin of human language would focus on the selective advantages that language conferred on the earliest humans (or protohumans). However, some thought about this matter will reveal that human language exhibits at least two characteristics that do not appear to confer any particular advantage on the survival of humans as a species.
First, human language, in terms of its structure and the rules that govern its use, is far more complex than would appear to be necessary to ensure effective communication. Consider these words written by psychologist David Premark and quoted by Ann Gauger at evolutionnew.org:
I challenge the reader to reconstruct the scenario that would confer selective fitness on recursiveness [the quality of having phrases embedded within phrases]. Language evolved, it is conjectured, at a time when humans or protohumans were hunting mastodons...Would it be a great advantage for one of our ancestors squatting alongside the embers, to be able to remark, "Beware of the short beast whose front hoof Bob cracked when, having forgotten his own spear back at camp, he got in a glancing blow with the dull spear he borrowed from Jack"?
Human language is an embarrassment for evolutionary theory because it is vastly more powerful than one can account for in terms of selective fitness. A semantic language with simple mapping rules of a kind one might suppose that the chimpanzee would have, appears to confer all the advantages one normally associates with discussions of mastodon hunting or the like. For discussions of that kind, syntactical classes, structure-dependent rules, recursion and the rest, are overly powerful devices, absurdly so. (as quoted in "Beyond Adaptation: The Human Brain Is Something New," evolutionnews.org, Sept. 18, 2018).
Indeed, as Gauger herself notes, "Life did not require complex sentences when 'Look out!' or 'Pass the meat,' would have done."
Second, language enables human beings to think and communicate about abstract objects like justice or truth. Animals are able to communicate about concrete objects, like an approaching predator, but they are not able discuss a concept like mercy. Indeed, as neurosurgeeon Michael Egnor points out:
The purpose of language is not primarily to communicate. The purpose of language is to enable man to think in a human way. Man alone is capable of abstract thought--thoughts about concepts that are universals, and not particular things. Man thinks about justice, and about mercy, about politics and imaginary numbers, and about countless concepts that are not particular physical things. This is abstract thought, and only humans think abstractly.
Animals are limited to thought about particulars. Dogs think about the food in their bowl. Humans think about nutrition. Dogs think about the good feeling they get when they are petted. Humans think about joy and love in an abstract sense. Both humans and animals have the capacity to think about particulars. Only humans also have the capacity to think about abstract concepts. ("How Is Human Language Different from Animal Signals?" mindmatters.ai, December 10, 2018).
However, we need to ask: what evolutionary advantage does an ability to think and speak of abstract objects confer on human beings? How would a capacity for language have enabled ancient humans to survive? It is difficult to find a plausible response to these questions--though I can imagine somebody has tried to!
In short, human language is more complex and confers more capabilities than would have been needed to ensure the survival of the species. Consequently, it is difficult to see how the emergence of language can be explained within an evolutionary framework, which makes me quite skeptical about the idea of "evolutionary linguistics."
Image of humans hunting mastodons from gizmodo.com