Social learning -by observing and copying others- is a highly successful cultural mechanism for adaptation, outperforming individual information acquisition and experience. Here, we investigate social learning in the context of the uniquely human capacity for reflective, analytical reasoning. A hallmark of the human mind is our ability to engage analytical reasoning, and suppress false associative intuitions. Through a set of lab-based network experiments, we find that social learning fails to propagate this cognitive strategy. When people make false intuitive conclusions, and are exposed to the analytic output of their peers, they recognize and adopt this correct output. But they fail to engage analytical reasoning in similar subsequent tasks. Thus, humans exhibit an 'unreflective copying bias,' which limits their social learning to the output, rather than the process, of their peers' reasoning -even when doing so requires minimal effort and no technical skill. In contrast to much recent work on observation-based social learning, which emphasizes the propagation of successful behavior through copying, our findings identify a limit on the power of social networks in situations that require analytical reasoning.