Normal anxiety is considered an adaptive response to the possible presence of danger, but it appears highly susceptible to dysregulation. Anxiety disorders are prevalent at high frequency in contemporary human societies, yet impose substantial disability upon their sufferers. This raises a puzzle: why has evolution left us vulnerable to anxiety disorders? We develop a signal detection model in which individuals must learn how to calibrate their anxiety response: they need to decide which cues indicate danger in the environment. We study the optimal strategy for doing so, and find that even when individuals learn optimally, a subset of the population over-reacts to mild cues, but no comparable subset under-reacts to strong signs of danger. In other words, a subset of the population exhibits undue anxiety. This phenomenon arises because when individuals become too cautious, they stop sampling the environment and fail to correct their misperceptions, whereas when individuals become too careless they continue to sample the environment and soon discover their mistakes. We suggest that this basic and inevitable consequence of optimal learning about how to interpret cues of possible danger may contribute to the problem of excessive anxiety in humans.