Communication about climate change has never been more urgent. But what if talking about a need for concern about climate change actually contributes to resistance against such concern? I argue that in an effort to stimulate concern and action, climate communicators often fail to listen and give respect to the values and experiences of publics who are unconcerned about climate change. Climate change narratives tend to pathologise unconcern as a negative and uniform attitude, without reflecting critically on the sources of these narratives beyond scientific facts. In shaping normative and unreflexive narratives of concern and failing to address the actual concerns and priorities of diverse publics, communicators can effectively co‐produce counter‐narratives. In response, in this article I share the stories of people who identify as unconcerned about climate change. Their narratives reveal processes of discursive friction between the concerned and the unconcerned, through which values, priorities, and assumptions are brought into conflict. Recognising and representing the messiness and plurality of attitudes to climate change could generate more useful forms of friction, shifting from antagonistic to agonistic and productive discourse. Avoiding polarised narratives of climate concern and unconcern is vital to enable a broader participation in diverse coalitions for climate action.