In the literature, the term code-mixing/switching refers to instances of language mixing in which speakers/signers combine properties of two or more languages in their utterances. Such a linguistic behavior is typically discussed in the context of multilinguals, and experts commonly focus on the form of language mixing/switching and its cross-linguistic commonalities. Not much is known, however, about how the knowledge of code-mixing comes about. How come any speaker/signer having access to more than one externalization channel (spoken or signed) code-mixes spontaneously? Likewise, why do both neurotypical speakers/signers and certain neuro-atypical speakers/signers produce structurally similar mixing types? This paper offers some answers to these questions arguing that the cognitive process underlying code-mixing is a basic property of the human learning device: recombination, a fully automated cognitive process. Recombination is innate: it allows learners to select relevant linguistic features from heterogeneous inputs, and recombine them into new syntactic objects as part of their mental grammars whose extensions, arguably individual idiolects, represents what Aboh (2015b, 2019a,b) characterizes as hybrid grammars.