This paper explores previous arguments that language evolved not from animal communication, as naturally assumed by most scholars, but instead out of animal cognition. It is proposed here that additional support for this argument comes from Cognitive Linguistics, an interdisciplinary branch of linguistics. Cognitive Linguistics mediates communication and cognition but, as with Cognitive Discourse Analysis, studies language use in terms of what it demonstrates about underlying cognitive processes and concepts. The paper demonstrates key examples of animal cognition’s links to language, with Cognitive Linguistics support, as well as the approach’s application to animal cognition in terms of domain-general symbolism, beyond verbal language. However, because communication remains a major function of language, the communicative aspect ought to be maintained in the explanation of language evolution.