Alliance theory finds its origins in Claude Levi-Strauss's Elementary Structures of Kinship (1949) and is stated explicitly in opposition to the functionalist theory of Radcliffe-Brown. The two frameworks explain the same recurring pattern, the cross-cultural preference for cross-cousin marriage, through incompatible mechanisms: exchange between descent groups versus the internal logic of descent and inheritance rules, and anthropology has not settled which framework better explains kinship systems generally.
What would resolve this A cross-cultural test capable of distinguishing exchange-driven from descent-driven kinship organization would need comparative ethnographic data across many historically unrelated kinship systems that the two frameworks predict differently, and both sides have so far read the same ethnographic record as supporting their own account, which is why this remains an interpretive rather than a narrowly empirical dispute.
OpenSocial and Cultural AnthropologyWikipedia: Alliance Theory