Kinship terminologies are the semantic systems of language that express kinship relations between individuals: in English, ‘aunt’ denotes a parent's sister. Theoretical models of kinship terminology diversity reduce over 10 billion possible organisations to six key types, each of which are hypothesised to be aligned with particular cultural norms of descent, marriage or residence patterns. Often, terminological type is used to infer social patterns in past societies based on these putative relationships between kinship terminologies and social structure, and these associations are staples of ‘Anthropology 101’. However, these relationships have not been scrutinised using modern comparative methods. Here we show that kinship terminologies vertically track language phylogeny in Austronesian, Bantu and Uto-Aztecan, three languages families of different time-depths and environments. We find no unidirectional or universal models of evolution in kinship terminology. Of 18 existing anthropological coevolutionary theories regarding kinship terminology and cultural practices across 176 societies, we find only patchy support, and no evidence for putative universal drivers of evolution in kinship terminologies.