The widespread potential for somatic fusion among different conspecific multicellular individuals suggests that such fusion is adaptive. However, because recognition of non-kin (allorecognition) usually leads to a rejection response, successful somatic fusion is limited to close kin. This is consistent with kin-selection theory, which predicts that the potential cost of fusion and the potential for somatic parasitism decrease with increasing relatedness. Paradoxically, however, Crozier found that, in the short term, positive-frequency-dependent selection eliminates the required genetic polymorphism at allorecognition loci. The 'Crozier paradox' may be solved if allorecognition is based on extrinsically balanced polymorphisms, for example at immune loci. Alternatively, the assumption of most models that self fusion is mutually beneficial is wrong. If fusion is on average harmful, selection will promote unconditional rejection. However, we propose that fusion within individuals is beneficial, selecting for the ability to fuse, but fusion between individuals on average costly, selecting for non-self recognition (rather than non-kin recognition). We discuss experimental data on fungi that are consistent with this hypothesis.