While most supervised learning algorithms follow rational pathways, efficiently mapping inputs to outputs and optimizing performance with impressive precision, they tend to overlook a quieter, often unconscious form of judgment: the kind humans rely on to navigate ambiguity, not through logic, but through intuition. We propose BayesIntuit, a reasoning neural framework that offers a novel alternative by emulating human intuition by learning to negotiate the balance between current perception and prior experience, guided by a self-adjusting sense of epistemic confidence in supervised classification tasks. BayesIntuit integrates a statistical inference module that captures signals of doubt, a dynamic memory system that informs current learning through accumulated context, and an adaptive control signal generated stochastically to reflect confidence in the blending of memory and perception, which also acts as an implicit form of learning regularization. BayesIntuit moves neural models beyond static data interpretation, toward a more adaptive, context-aware mode of reasoning, one that mimics the intuitive judgment humans deploy, contributing to the pursuit of interpretable, human-aligned AI, where reasoning is not only effective, but traceable.