This research paper investigates the impact of different language models (LLMs) used as "teachers" to generate synthetic responses for instruction tuning. The authors demonstrate a surprising phenomenon they call the "Larger Models' Paradox," where larger and supposedly "stronger" teacher models do not always lead to improved instruction-following abilities in smaller base models. They propose a novel metric called Compatibility-Adjusted Reward (CAR) to better predict the effectiveness of teacher models, taking into account the compatibility between the teacher and the base model being fine-tuned. The study challenges the common assumption that larger LLMs are always better teachers and suggests that a more nuanced understanding of compatibility is needed for successful instruction tuning.