Among the long-standing efforts to elucidate the physical mechanisms of protein–ligand catch bonding, particular attention has been directed at the family of selectin proteins. Selectins exhibit slip, catch-slip, and slip-catch-slip bonding, with minor structural modifications causing major changes in selectins’ response to force. How can a single structural mechanism allow interconversion between these various behaviors? We present a unifying theory of selectin-ligand catch bonding, using a structurally-motivated free energy landscape to show how the topology of force-induced deformations of the molecular system produce the full range of observed behaviors. Our novel approach can be applied broadly to other protein–ligand catch bonds, and our results have implications for such future models. In particular, our model exhibits a severe breakdown of Bell’s theory—a paradigmatic theory that is widely invoked in theories of catch bonding. This raises questions about the suitability of Bell’s theory in modeling other catch bonds.