High pathogenicity avian influenza viruses (HPAIVs) emerge from H5 and H7 low-pathogenicity avian influenza virus progenitors through mutations that introduce a multibasic cleavage site in haemagglutinin. Although nucleotide insertions recurrently generate this motif, the molecular determinants of insertion and whether particular HA sequences are genetically predisposed to evolve toward HPAIV remain unknown. Combining experimental virology and thermodynamic modelling, we show that insertions arise through polymerase slippage controlled by local product-template duplex thermodynamics within the viral polymerase catalytic site. Predicted RNA secondary structures outside the polymerase are not required for high-frequency insertions and only modestly modulate insertion rates. We formalize this mechanism in HPAIVpredict, which predicts insertion profiles, recapitulates intermediates associated with documented HPAIV emergence events and identifies H5 and H7 sequence backgrounds predisposed to acquire functional multibasic cleavage sites.