Medical imaging provides essential visual insights for diagnosis, and multimodal large language models (MLLMs) are increasingly utilized for its analysis due to their strong generalization capabilities; however, the underlying factors driving this generalization remain unclear. Current research suggests that multi-task training outperforms single-task as different tasks can benefit each other, but they often overlook the internal relationships within these tasks. To analyze this phenomenon, we attempted to employ compositional generalization (CG), which refers to the models' ability to understand novel combinations by recombining learned elements, as a guiding framework. Since medical images can be precisely defined by Modality, Anatomical area, and Task, naturally providing an environment for exploring CG, we assembled 106 medical datasets to create Med-MAT for comprehensive experiments. The experiments confirmed that MLLMs can use CG to understand unseen medical images and identified CG as one of the main drivers of the generalization observed in multi-task training. Additionally, further studies demonstrated that CG effectively supports datasets with limited data and confirmed that MLLMs can achieve CG across classification and detection tasks, underscoring its broader generalization potential. Med-MAT is available at https://github.com/FreedomIntelligence/Med-MAT.