Anxiety disorders are characterized by a range of aberrations in the processing of and response to threat, but there is little clarity what core pathogenesis might underlie these symptoms. Here we propose that a particular set of unrealistically pessimistic assumptions can distort an agent's behavior and underlie a host of seemingly disparate anxiety symptoms. We formalize this hypothesis in a decision theoretic analysis of maladaptive avoidance and a reinforcement learning model, which shows how a localized bias in beliefs can formally explain a range of phenomena related to anxiety. The core observation, implicit in standard decision theoretic accounts of sequential evaluation, is that the potential for avoidance should be protective: if danger can be avoided later, it poses less threat now. We show how a violation of this assumption - via a pessimistic, false belief that later avoidance will be unsuccessful - leads to a characteristic, excessive propagation of fear and avoidance to situations far antecedent of threat. This single deviation can explain a range of features of anxious behavior, including exaggerated threat appraisals, fear generalization, and persistent avoidance. Simulations of the model reproduce laboratory demonstrations of abnormal decision making in anxiety, including in situations of approach-avoid conflict and planning to avoid losses. The model also ties together a number of other seemingly disjoint phenomena in anxious disorders. For instance, learning under the pessimistic bias captures a hypothesis about the role of anxiety in the later development of depression. The bias itself offers a new formalization of classic insights from the psychiatric literature about the central role of maladaptive beliefs about control and self-efficacy in anxiety. This perspective also extends previous computational accounts of beliefs about control in mood disorders, which neglected the sequential aspects of choice.