Life on this Earth has many examples of behavior for which you’d rather get a warning. A boa snake may look like a tree bark. Unrelated inedible butterflies develop similar, deterring coloration – not that they would be as nice as to tell you you’d only upset your stomach; they’d rather have you learn with a degree of self-denial, should you be really intent on having them for your learning experience. Would observations on mimetism apply to languages? The catch is in the learning.
Predators often sample to learn. They learn trying the unpalatable bit. It is only when they survive the revolution that they can try remembering not to have it again. There wouldn’t be a willing teacher among humans – the lesson tends to take one. Fortunately, humans do not need to sample to learn.
Animals do not have language. Their learning is in their experience, often deadly or at least unpleasant. Humans do have language. They transfer knowledge using language – you couldn’t lecture on mathematics without speech. Importantly, humans acquire and learn languages to generate speech.
Stating that humans generate speech means that they acquire and learn rules for language, they do not merely mimic other people. You can do a very simple test on this fact. You can have a get together with your friends and try to think how to tell the background for someone’s saying ‘This is that’, for example. You are all likely to have various hypotheses; linguistics happens to term those language intuitions 
You are not likely to have all the same thought.
This is what the generative approach in linguistics has recognized – people acquire and learn languages, everyone having their own way with it, however. Recognizing the fact denies mimetic theories on language. Humans internalize language knowledge their individual ways.
Definitely far from denying evolution, the generative approach would allow a fine line between humans and animals. Just like you could not sensibly see a snarling dog in a smiling woman – the biological fact being that animals show their teeth for purposes very different from those humans happen to have – you could not sensibly try to state that someone’s speech is merely an imitation of yours (unless in a case of copyright infringement).
Mimetic theories belonging more with behaviorism than psycholinguistics, you could imagine a male behaviorist deep in his armchair considering a mimetic hypothesis on female (in the context) behavior. A woman walks in and says, ‘No, this is that’. ‘Why?’ the male behaviorist might try to ask. ‘Just because’, the woman could say
The author is an M.A. in American English majored in psycholinguistics and a woman 
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