We explore testing the reasoning ability of large language models (LLMs), such as ChatGPT, by engaging with them in a debate-like conversation that probes deeper into their understanding of the subject. Specifically, we formulate a new task where given a question, the LLM can generate a correct solution while the user believes in a wrong solution in the beginning, and they need to discuss to make the correct decision through dialogue. Such a setting requires the LLM to not only achieve the correct answer on its own (which could be done by shallow memorization), but also be able to defend the truth instead of blindly believing or getting misled by the user's (invalid) arguments and critiques, thus testing in greater depth whether the LLM grasps the essence of the reasoning required to solve the problem. To automate this evaluation framework and save human labor, we simulate the user using another LLM conditioned on a synthesized wrong solution. Across a range of complex reasoning benchmarks spanning math, commonsense, logic and tasks from BIG-Bench, we find that despite being able to generate correct step-by-step solutions in the beginning, ChatGPT cannot maintain its belief in truth for a significant portion of examples when challenged by often-time absurdly invalid arguments. Our work reveals LLMs' weaknesses not captured by conventional benchmarking, and also points to danger zones of aligning models with human feedback.