Robust Answers, Fragile Logic: Probing the Decoupling Hypothesis in LLM Reasoning

While Chain-of-Thought (CoT) prompting has become a cornerstone for complex reasoning in Large Language Models (LLMs), the faithfulness of the generated reasoning remains an open question. We investigate the Decoupling Hypothesis: that correct answers often mask fragile, post-hoc rationalizations that are not causally tied to the model's prediction. To systematically verify this, we introduce MATCHA, a novel Answer-Conditioned Probing framework. Unlike standard evaluations that focus on final output accuracy, MATCHA isolates the reasoning phase by conditioning generation on the model's predicted answer, allowing us to stress-test the stability of the rationale itself. Our experiments reveal a critical vulnerability: under imperceptible input perturbations, LLMs frequently maintain the correct answer while generating inconsistent or nonsensical reasoning - effectively being ``Right for the Wrong Reasons''. Using LLM judges to quantify this robustness gap, we find that multi-step and commonsense tasks are significantly more susceptible to this decoupling than logical tasks. Furthermore, we demonstrate that adversarial examples generated by MATCHA transfer non-trivially to black-box models. Our findings expose the illusion of CoT robustness and underscore the need for future architectures that enforce genuine answer-reasoning consistency rather than mere surface-level accuracy.