This paper investigates the reliability of explanations generated by large language models (LLMs) when prompted to explain their previous output. We evaluate two kinds of such self-explanations – extractive and counterfactual – using three state-of-the-art LLMs (2B to 8B parameters) on two different classification tasks (objective and subjective). Our findings reveal that, while these self-explanations can correlate with human judgement, they do not fully and accurately follow the model’s decision process, indicating a gap between perceived and actual model reasoning. We show that this gap can be bridged because prompting LLMs for counterfactual explanations can produce faithful, informative, and easy-to-verify results. These counterfactuals offer a promising alternative to traditional explainability methods (e.g. SHAP, LIME), provided that prompts are tailored to specific tasks and checked for validity.