Linguistic animacy reflects a particular construal of biological distinctions encountered in the world, passed through cultural and cognitive filters. This study explores the process by which our construal of animacy becomes encoded in the grammars of human languages. We ran an iterated learning experiment investigating the effect of animacy on language transmission. Participants engaged in a simple artificial language learning task in which they were asked to learn which affix was assigned to each noun in the language. Though initially random, the language each participant produced at test became the language that the subsequent participant in a chain was trained on. Results of the experiment were analysed in terms of learnability, measured through the accuracy of responses, and structure, using an entropy measure. We found that the learnability of languages increased over generations, as expected, but entropy did not decrease. Languages did not become formally simpler over time. Instead, structure emerged through a reorganisation of noun classes around animacy-based categories. The use of semantic animacy distinctions allowed languages to retain morphological complexity while becoming more learnable. Our study shows that grammatical reflexes of animacy distinctions can arise out of learning alone, and that structuring grammar based on animacy can make languages more learnable.