Large Language Models (LLMs) are becoming vital tools that help us solve and understand complex problems by acting as digital assistants. LLMs can generate convincing explanations, even when only given the inputs and outputs of these problems, i.e., in a ``black-box'' approach. However, our research uncovers a hidden risk tied to this approach, which we call *adversarial helpfulness*. This happens when an LLM's explanations make a wrong answer look right, potentially leading people to trust incorrect solutions. In this paper, we show that this issue affects not just humans, but also LLM evaluators. Digging deeper, we identify and examine key persuasive strategies employed by LLMs. Our findings reveal that these models employ strategies such as reframing the questions, expressing an elevated level of confidence, and cherry-picking evidence to paint misleading answers in a credible light. To examine if LLMs are able to navigate complex-structured knowledge when generating adversarially helpful explanations, we create a special task based on navigating through graphs. Some LLMs are not able to find alternative paths along simple graphs, indicating that their misleading explanations aren't produced by only logical deductions using complex knowledge. These findings shed light on the limitations of black-box explanation setting. We provide some advice on how to use LLMs as explainers safely.