Clinical decision support requires not only correct answers but also clinically valid reasoning. We propose Differential Reasoning Learning (DRL), a framework that improves clinical agents by learning from reasoning discrepancies. From reference reasoning rationales (e.g., physician-authored clinical rationale, clinical guidelines, or outputs from more capable models) and the agent's free-form chain-of-thought (CoT), DRL extracts reasoning graphs as directed acyclic graphs (DAGs) and performs a clinically weighted graph edit distance (GED)-based discrepancy analysis. An LLM-as-a-judge aligns semantically equivalent nodes and diagnoses discrepancies between graphs. These graph-level discrepancy diagnostics are converted into natural-language instructions and stored in a Differential Reasoning Knowledge Base (DR-KB). At inference, we retrieve top-$k$ instructions via Retrieval-Augmented Generation (RAG) to augment the agent prompt and patch likely logic gaps. Evaluation on open medical question answering (QA) benchmarks and a Return Visit Admissions (RVA) prediction task from internal clinical data demonstrates gains over baselines, improving both final-answer accuracy and reasoning fidelity. Ablation studies confirm gains from infusing reference reasoning rationales and the top-$k$ retrieval strategy. Clinicians' review of the output provides further assurance of the approach. Together, results suggest that DRL supports more reliable clinical decision-making in complex reasoning scenarios and offers a practical mechanism for deployment under limited token budgets.