Net Zero is the dominant framework for organising health system decarbonisation. Yet throughout Net Zero's rise to prominence, greenhouse gas emissions have remained on a dangerous trajectory. In this analysis, we synthesise strands of Net Zero critique from the climate policy literature, examine their implications for health systems and briefly present an alternative framework for decarbonisation. We begin by reviewing three families of Net Zero critique which have, to date, received little attention in the sustainable healthcare space: unambitious and inequitable pledges, accounting failures, and structural problems with the framework itself. Together, these critiques challenge the idea that the Net Zero agenda is best positioned to deliver upon the Paris Agreement commitment to limit temperature rise to below 1.5°C-2°C. We then consider how each challenge manifests in the health sector with examples from state and non-state actors. Finally, we briefly introduce an alternative 'reduce and support' approach which aims to address some of Net Zero's weaknesses. Reduce-and-support represents a conceptual pivot that would extend current best practices in science-based mitigation targets while exchanging the atomised trading of problematic carbon offsets for resource pooling towards collective efforts at deep decarbonisation. We discuss the moral, political and practical advantages of this framework and identify areas for future work. By considering the adoption of reduce-and-support, health systems can provide leadership for ratcheting climate ambition at this pivotal moment of accelerating climate breakdown.