Extensive research into public attitudes about climate change commonly portrays those who do not express concern about this issue as unwitting victims of their own or others’ biases. Characterised as apathy, ignorance, scepticism or denial, absence of concern about climate change has been presented as being rooted in an individual’s lack of considered engagement with scientific reasons for concern. This ‘concern deficit’ is framed as a problem to be addressed through policy, education and communication that seeks to maximise concern about climate change. In contrast, we conceptualise unconcern about climate change as an expression of focal life concerns that are incommensurable with dominant narratives of climate change. Originating in active cognitive, social and experiential processes, we regard unconcern about climate change as inseparable from the lived contexts in which it is expressed and irreducible to the attitudes or attributes of individuals. Using narrative analysis of repeat in-depth interviews with Australians who express unconcern about climate change, we find that this unconcern has multiple sources, takes diverse forms and is entangled in epistemological and normative engagements with other issues. It is constituted through social relationships, discursive processes, moral values and embodied experiences that are overlooked in much existing research. We argue that respectful attention to the experiential conditions in which concern about climate change is resisted can enable constructive re-negotiation of narratives of climate change. Such agonistic processes could lead to more reflexive, pluralist and dialogical forms of discourse that better articulate climate science and policy with a wider diversity of lived concerns.