The Greeks, like the Egyptians, became rich from trade from the surplus of great farming. The wealthy had lots of time on their hands to educate themselves and develop new ideas. They also traded knowledge with people across seas and from other civilisations which gave them new ideas and theories to explore.
The Greeks didn't just study medical ideas, they educated themselves with just about everything. The Greeks were great thinkers and had the time to think because they were rich because of the surplus of farming. They began developing theories in mats, geometry, science, geometry, politics etc.
The Greeks still believed in the Gods but preferred to find more rational explanations for things.
The theory of the four humours was the first well-thought-out, early scientific idea. Hippocrates was a great Greek thinker, and realised that diseases were caused by natural things and should be treated naturally. The Greeks began to move away from supernatural ideas about the causes of illness and moved towards a more logical approach. Magical causes of illness could not be proved. Greek doctors observed their patients and saw they often had a liquid coming out of their body ie vomiting to bring up bile. It seemed as though, when someone was ill, a liquid was coming out of the body because they had too much of this liquid in them. The body was getting rid of the liquid to restore the balance. This idea also fit in nicely with the Greek idea that everything was made up of the the four elements. It seemed only natural that they would think the body was made up of four things: Phlegm, Black Bile, Yellow Bile and Blood.
The theory of the four humours was Hippocrates idea.
The theory of the four humours led to the elements and seasons being discovered, which we still use today. They realised that:
Winter ---> Phlegm (runny noses) ---> Water (moist and wet)
Autumn ---> Black Bile (vomit, dry skin) ---> Earth (cold and dry)