Fallacies are not only part and parcel of human communication, they are also important for generative models in that fallacies can be tailored to self-verify the output they generate. Previous work has shown that fallacy detection and classification is tricky, but the question that still remains is whether the use of theoretical explanations in prompting Large Language Models (LLMs) on the task enhances the performance of the models. In this paper we show that this is not the case: Using the pragma-dialectics approach to fallacies (van Eemeren, 1987), we show that three GPT models struggle with the task. Based on our own PD-oriented dataset of fallacies and an extension of an existing fallacy dataset from Jin et al. (2022), we show that this is not only the case for fallacies “in the wild”, but also for textbook examples of fallacious arguments. Our paper also supports the claim that LLMs generally lag behind in fallacy classification in comparison to smaller-scale neural models.