Tipping points have gained substantial traction in climate change discourses, both as representing the possibility of catastrophic and irreversible physical and societal impacts and as a way to set in motion positive, rapid and self-sustaining responses, such as the adoption of new technologies, practices, and behaviors. As such, tipping points appear ubiquitous in natural and social systems. Here, we critique 'tipping point' framings, specifically their insufficiency for describing the diverse dynamics of complex systems; their reductionist view of individuals, their agency and their aspirations; and their tendency to convey urgency without fostering a meaningful basis for climate action. We argue for clarifying the scientific discussion of the phenomena lumped under the 'tipping point' umbrella by using more specific language to capture relevant aspects (e.g., irreversibility, abruptness, self-amplification, potential surprise) and for the critical evaluation of whether, how and why the different framings can support accurate scientific understanding and effective climate risk management. Multiple social scientific frameworks suggest that deep uncertainty and perceived abstractness associated with many proposed Earth system 'tipping points' make them both unlikely to provoke effective action and not helpful for setting governance goals that must be sensitive to multiple constraints. The mental model of a 'tipping point' does not align with the multifaceted nature of social change; a broader focus on the dynamics of social transformation is more useful. Temperature-based benchmarks originating in a broad portfolio of concerns already provide a suitable guide for global mitigation policy targets and should not be confused with physical thresholds of the climate system.