Adapting Large Language Models (LLMs) to specialized domains without human-annotated data is a crucial yet formidable challenge. Widely adopted knowledge distillation methods often devolve into coarse-grained mimicry, where the student model inefficiently targets its own weaknesses and risks inheriting the teacher's reasoning flaws. This exposes a critical pedagogical dilemma: how to devise a reliable curriculum when the teacher itself is not an infallible expert. Our work resolves this by capitalizing on a key insight: while LLMs may exhibit fallibility in complex, holistic reasoning, they often exhibit high fidelity on focused, atomic sub-problems. Based on this, we propose Divergence-Guided Reasoning Curriculum (DGRC), which constructs a learning path from atomic knowledge to reasoning chains by dynamically deriving two complementary curricula from disagreements in reasoning pathways. When a student and teacher produce conflicting results, DGRC directs the teacher to perform a diagnostic analysis: it analyzes both reasoning paths to formulate atomic queries that target the specific points of divergence, and then self-answers these queries to create high-confidence atomic question-answer pairs. These pairs then serve a dual purpose: (1) providing an atomic curriculum to rectify the student's knowledge gaps, and (2) serving as factual criteria to filter the teacher's original reasoning chains, yielding a verified CoT curriculum that teaches the student how to integrate atomic knowledge into complete reasoning paths. Experiments across the medical and legal domains on student models of various sizes demonstrate the effectiveness of our DGRC framework. Notably, our method achieves a 7.76% relative improvement for the 1.5B student model in the medical domain over strong unlabeled baseline.