Cognition is not passive data accumulation but the active resolution of uncertainty through symmetry breaking. This paper argues that both cognitive evolution and development unfold via sequential symmetry-breaking transitions that disrupt innate regularities across space, time, self, and representation. First, spatial symmetry is broken through bilateral body plans and neural codes like grid and place cells, which privilege egocentric orientation and localized encoding. Second, reinforcement learning introduces temporal asymmetry by favoring future rewards, establishing a directional flow of inference. Third, goal-directed simulation breaks spatiotemporal symmetry between internal self-models and the external world, enabling embodied inference and solving the combinatorial search problem. Fourth, social cognition via mentalizing and imitation breaks the symmetry between minds, allowing agents to infer others' beliefs. Finally, language imposes a linear, recursive structure onto unordered thought, breaking expressive symmetry through syntax and grammar. These asymmetries are unified by the Context-Content Uncertainty Principle (CCUP), which frames cognition as a cyclical entropy-minimizing process. At the core lies the principle of structure-before-specificity: ambiguous input is first mapped onto stable latent structures before being bound to specific instances. This promotes generalization, reduces sample complexity, and prevents overfitting. Inverting inference, from content back to context, further breaks the curse of dimensionality by constraining inference to goal-consistent manifolds. Thus, symmetry breaking is not incidental but the foundational mechanism by which cognition organizes, stabilizes, and scales intelligent behavior in an uncertain and dynamic world.