The integration of Large Language Models (LLMs) into clinical decision support is critically obstructed by their opaque and often unreliable reasoning. In the high-stakes domain of healthcare, correct answers alone are insufficient; clinical practice demands full transparency to ensure patient safety and enable professional accountability. A pervasive and dangerous weakness of current LLMs is their tendency to produce "correct answers through flawed reasoning." This issue is far more than a minor academic flaw; such process errors signal a fundamental lack of robust understanding, making the model prone to broader hallucinations and unpredictable failures when faced with real-world clinical complexity. In this paper, we establish a framework for trustworthy clinical argumentation by adapting the Toulmin model to the diagnostic process. We propose a novel training pipeline: Curriculum Goal-Conditioned Learning (CGCL), designed to progressively train LLM to generate diagnostic arguments that explicitly follow this Toulmin structure. CGCL's progressive three-stage curriculum systematically builds a solid clinical argument: (1) extracting facts and generating differential diagnoses; (2) justifying a core hypothesis while rebutting alternatives; and (3) synthesizing the analysis into a final, qualified conclusion. We validate CGCL using T-Eval, a quantitative framework measuring the integrity of the diagnosis reasoning. Experiments show that our method achieves diagnostic accuracy and reasoning quality comparable to resource-intensive Reinforcement Learning (RL) methods, while offering a more stable and efficient training pipeline.