We consider the general problem of absolute discrimination between categories of ligands irrespective of their concentration. An instance of this problem is immune discrimination between self and not-self. We connect this problem to biochemical adaptation, and establish that ligand antagonism – the ability of sub threshold ligands to negatively impact response – is a necessary consequence of absolute discrimination.Thus antagonism constitutes a “phenotypic spandrel”: a phenotype existing as a necessary by-product of another phenotype. We exhibit a simple analytic model of absolute discrimination displaying ligand antagonism, where antagonism strength is linear in distance from threshold. This contrasts with proofreading based models, where antagonism vanishes far from threshold and thus displays an inverted hierarchy of antagonism compared to simple model . The phenotypic spandrel studied here is expected to structure many decision pathways such as immune detection mediated by TCRs and FcϵRIs.