The six‐dimensional HEXACO model of personality structure and its associated inventory have increasingly been used in personality research. But in spite of the evidence supporting this structure and demonstrating its advantages over five‐dimensional models, some researchers continue to use and promote the latter. Although there has been little overt, organized argument against the adoption of the HEXACO model, we do hear sporadic offerings of reasons for retaining the five‐dimensional systems, usually in informal conversations, in manuscript reviews, on social media platforms, and occasionally in published works. In this target article, we list all of the objections to the HEXACO model that we have heard of, and we then explain why each objection fails. © 2020 European Association of Personality Psychology