Economic experiments, and evolutionary models, have suggested that human cooperation is sustained by altruistically motivated cooperators paying to punish non-cooperators. Consequently, punishment allows cooperators to happily match each other (conditionally cooperate), confident that they will not be exploited by non-cooperators. However, it is not clear that punishment is altruistically motivated, and previous experiments have confounded a fear of being punished with being surrounded by cooperators. Here, we experimentally decouple the fear of punishment from a cooperative environment and allow cooperation and punishment to freely separate (420 participants). We show, that if a minority of individuals are made immune to punishment, they (1) learn to stop cooperating despite being surrounded by high levels of cooperation; and (2) continue to punish, ‘hypocritically’, showing that cooperation and punishment do not form one, altruistically motivated, linked trait. Overall, 48% of punishers were ‘anti-social’ during the experiment, suggesting humans are not in general altruistic punishers.