Meme, as a multi-modal content with viral spread, has become a powerful tool for ideological propaganda through implicit narration. These content pieces often encode propagandistic intents via implicit multimodal conflicts and construct persuasive narratives beyond literal meanings. However, existing methods for detecting the propagandistic nature of memes generally face challenges such as insufficient implicit semantic capture and weak reasoning interpretability. Inspired by the success of large language models (LLMs) in complex reasoning tasks, we propose a three-stage framework that synergizes LLMs distillation with reinforcement learning to bridge this gap. First, we reformulate detection as a generative rationale extraction task, distilling reasoning into student model via pseudo rationale alignment. Second, we introduce DPO-based preference optimization to calibrate reasoning paths and mitigate hallucination risks. Finally, task-specific fine-tuning adapts the model to binary classification. Evaluations on the propaganda meme benchmark demonstrated that the proposed framework outperformed the current state-of-the-art models, achieving an F1-score of 0.8833.