What role does non-genetic inheritance play in evolution? In recent work we have independently and collectively argued that the existence and scope of non-genetic inheritance systems, including epigenetic inheritance, niche construction/ecological inheritance, and cultural inheritance extemdash alongside certain other theory revisions extemdash necessitates an extension to the neo-Darwinian Modern Synthesis (MS) in the form of an Extended Evolutionary Synthesis (EES). However, this argument has been challenged on the grounds that non-genetic inheritance systems are exclusively proximate mechanisms that serve the ultimate function of calibrating organisms to stochastic environments. In this paper we defend our claims, pointing out that critics of the EES (1) conflate non-genetic inheritance with early 20th-century notions of soft inheritance; (2) misunderstand the nature of the EES in relation to the MS; (3) confuse individual phenotypic plasticity with trans-generational non-genetic inheritance; (4) fail to address the extensive theoretical and empirical literature which shows that non-genetic inheritance can generate novel targets for selection, create new genetic equilibria that would not exist in the absence of non-genetic inheritance, and generate phenotypic variation that is independent of genetic variation; (5) artificially limit ultimate explanations for traits to gene-based selection, which is unsatisfactory for phenotypic traits that originate and spread via non-genetic inheritance systems; and (6) fail to provide an explanation for biological organization. We conclude by noting ways in which we feel that an overly gene-centric theory of evolution is hindering progress in biology and other sciences.