Large Language Models (LLMs) are increasingly used to generate fact-checking explanations, but evaluating how faithful these justifications are remains a major challenge. In this paper, we examine how well four popular automatic metrics—G-Eval, UniEval, FactCC, and QAGs—capture faithfulness compared to expert-written explanations. We look at how these metrics agree with each other, how they correlate with explanation similarity, and how they respond to controlled errors.Our findings show that while some metrics like UniEval and FactCC show some sensitivity to noise and partial alignment with expert reasoning, none of them reliably catch hallucinations or consistently reflect true faithfulness. Manual analysis also reveals that metric behavior varies depending on the type and structure of the claim. Overall, current metrics are only moderately effective and often biased toward the style of LLM-generated text. This study points to the need for more reliable, context-aware evaluation methods and offers practical insights for improving how we measure faithfulness in fact-checking tasks.