Answer:
Because medicine in ancient Greece had a holistic perspective or a tradition healing holistic system, which was centered on natures and balance. Its founder was Hippocrates, who taught and searched the harmony between health, medicine and cosmos.
This holistic was advanced, the only system that was similarly improved was the Chinese, because they also considered medicine as a holistic subject. It's important to say that this perspective was replicated and used by western hemisphere.
However, this natural, cosmological perspective of medicine was changed by a more scientific approach, which created modern medicine science.