Stance detection aims to identify the attitude expressed in text towards a given target, with applications in public opinion analysis and misinformation mitigation. Despite recent advances in large language models (LLMs), two key challenges remain: (1) spurious correlations between superficial features and stance labels, and (2) lack of cognitive modeling that simulates the transition from intuitive perception to deliberate reasoning. To address these issues, we propose Cognitive-Driven Stance Detection (CDSD), inspired by Kahneman’s Dual-Process Theory. CDSD integrates fast intuitive judgment (System 1) and analytical reasoning (System 2), enhanced by three key modules: attention-based cognitive alignment to compare system focus, uncertainty-aware belief update using Bayesian inference, and self-doubt-triggered counterfactual reasoning for re-evaluation under low consistency or high uncertainty. Experimental results on SEM16, P-Stance, and VAST show that CDSD outperforms state-of-the-art methods across multiple LLMs. Notably, CDSD exhibits strong robustness against textual perturbations such as emotional word removal and rhetorical restructuring. By integrating cognitive theory with NLP, our work provides a promising path toward more reliable and interpretable stance detection systems.