Disagreement detection is a crucial task in natural language processing (NLP), particularly in analyzing online discussions and social media content. Large language models (LLMs) have demonstrated significant advancements across various NLP tasks. However, the performance of LLM in disagreement detection is limited by two issues: *conceptual gap* and *reasoning gap*. In this paper, we propose a novel two-stage framework, Concept Alignment and Reasoning Enhancement (CARE), to tackle the issues. The first stage, Concept Alignment, addresses the gap between expert and model by performing **sub-concept taxonomy extraction**, aligning the model’s comprehension with human experts. The second stage, Reasoning Enhancement, improves the model’s reasoning capabilities by introducing curriculum learning workflow, which includes **rationale to critique** and **counterfactual to detection** for reducing spurious association. Extensive experiments on disagreement detection task demonstrate the effectiveness of our framework, showing superior performance in zero-shot and supervised learning settings, both within and across domains.