One of the key challenges in programming education is being able to provide high-quality feedback to learners. Such feedback often includes explanations of the issues in students’ programs coupled with suggestions on how to fix these issues. Large language models (LLMs) have recently emerged as valuable tools that can help in this effort. In this article, we explore the relationship between the program repair ability of LLMs and their proficiency in providing natural language explanations of coding mistakes. We outline a benchmarking study that evaluates leading LLMs (including open-source ones) on program repair and explanation tasks. Our experiments study the capabilities of LLMs both on a course level and on a programming concept level, allowing us to assess whether the programming concepts practised in exercises with faulty student programs relate to the performance of the models. Our results highlight that LLMs proficient in repairing student programs tend to provide more complete and accurate natural language explanations of code issues. Overall, these results enhance our understanding of the role and capabilities of LLMs in programming education. Using program repair as a proxy for explanation evaluation opens the door for cost-effective assessment methods.