If a doctor is trying to decide whether or not to provide a medical treatment, does it matter ethically whether that treatment has already been started? Health professionals sometimes find it harder to stop a treatment (withdraw) than to refrain from starting the treatment (withhold). But does that feeling correspond to an ethical difference? In this article, we defend equivalence—the view that withholding and withdrawal of treatment are ethically equivalent when all other factors are equal. We argue that preference for withholding over withdrawal could represent a form of cognitive bias—withdrawal aversion. Nevertheless, we consider whether there could be circumstances in which there is a moral difference. We identify four examples of conditional nonequivalence. Finally, we reflect on the moral significance of diverging intuitions and the implications for policy. We propose a set of practical strategies for helping to reduce bias in end-of-life decision making, including the equivalence test.