On one hand, kinship is a universal human phenomenon that tends to align with biological relatedness, which might suggest evolutionary foundations. On the other hand, kinship has exceptional variation across the human populations, which points to cultural foundations. Furthermore, even if its foundation was biological, kinship is often too imprecise to track genetic relatedness efficiently, while inclusive fitness theory would suggest focusing only on the closest relatives, which is not the case in most human cultures. It was the parallel validity of these contradicting arguments that led to decades of fierce debate about the definition and measurement of the phenomenon. This paper offers a new approach to kinship. First, the model demonstrates that it is possible to generate kinship networks (a) derived from the kind of basic kin connections that our species shares with other apes, but (b) driven by network rather than biological logic beyond the immediate family. Second the model demonstrates that kinship as a network heuristic works efficiently only in high fertility societies, and gives way to similarity-based friendship with demographic transition. The results explain (i) why kinship labelling is unique to our species, (ii) why kinship is universal among human cultures, (iii) why kinship terminology systems are varied across cultures, (iv) why linguistic kin assignment is imprecise, and (v) why kinship is replaced by homophily when relatives are scarce. The model offers a unifying framework to the debate between social and evolutionary anthropology concerning the concept of human kinship.