Large language models (LLMs) excel at many tasks, but can they truly reason and argue like humans? A new study explores this question by testing LLMs on argumentation computation within abstract argumentation frameworks (AAFs). These frameworks represent arguments and their relationships as graphs, allowing researchers to analyze the LLM's ability to determine the 'acceptability' of different arguments based on complex interactions. The study constructed a benchmark dataset of AAFs with varying complexities and fine-tuned LLMs on two key tasks: computing 'grounded' and 'complete' extensions. These extensions represent sets of arguments that can be accepted simultaneously. Surprisingly, simply providing the AAF wasn't enough for the LLMs to excel. Adding step-by-step explanations of the reasoning process dramatically improved the LLM's accuracy and, importantly, its ability to generalize to more complex frameworks it hadn't seen before. This highlights the critical role of explainability, not just for understanding the LLM's decisions but also for improving its learning. While specialized graph neural networks still outperform LLMs on this specific task, the ability of LLMs to explain their reasoning offers a transparency advantage. This research opens up exciting possibilities for using LLMs in areas requiring complex reasoning, like legal decision-making or policy analysis. However, it also underscores the ongoing challenge of developing truly robust and human-like reasoning capabilities in AI. The next step? Exploring more nuanced argumentation semantics and developing even more sophisticated methods to teach LLMs how to argue effectively.