Safety-aligned large language models (LLMs) face a dilemma between helpfulness and harmlessness, where LLMs are expected to refuse harmful requests while remaining helpful by explaining their decisions. In this work, we observe a phenomenon caused by this dilemma. When asked to explain a refusal triggered by a harmful query, LLMs disclose exploitable elements in their refusal explanations. These elements allow attackers to induce the generation of harmful content. We formalize this vulnerability as Induced Refusal Explication (IRE). To identify and exploit IRE, we propose Explication of Refusal (EoR), a black-box and multi-turn jailbreak method with a dual-agent framework. EoR induces and analyzes refusal explanations from victim models and then generates follow-up queries to jailbreak them. We evaluate EoR across nine victim models. EoR achieves an average attack success rate (ASR) of **37.05** within five turns. When we apply EoR to the queries that PAIR fails to jailbreak, EoR reaches an average ASR of **66.0** across the nine victim models, which demonstrates that exploiting refusal explanations is complementary to existing automated jailbreak methods. We release our data and code at https://anonymous.4open.science/r/EoR-6234.