The symbiosis between reef-building corals and their algae endosymbionts is sensitive to temperature stress, which makes coral reefs vulnerable to climate change. However, a precise understanding of the capacity for the symbiosis to adapt to climate change is currently restricted by the lack of coherent explanation for the set of cellular events leading to its warm-water breakdown (= coral bleaching). Here, a new coral bleaching model is proposed in which the triggering event is a disruption to the ‘dark’ photosynthetic reactions of the algae endosymbionts, primarily due to a limited availability of CO₂ substrate around the Rubisco enzyme (ribulose-1,5-bisphosphate carboxylase). Paradoxically, this CO₂-limiting condition may be enhanced by the modern increase in atmospheric CO₂ partial pressure (pCO₂). Importantly, the model delivers a new standpoint from which to explain: (i) upper thermal bleaching thresholds; and (ii) the mechanism underpinning endosymbiont shuffling. Overall, the model leaves little doubt as to the diminished stability and functioning (i.e. resilience) of the coral–algae endosymbiosis due to the rising pCO₂ and warming trend in the upper ocean surface layer. It is concluded that whole-colony bleaching is the destructive endpoint to a suite of cellular processes that operate near continuously in modern symbiotic corals.