Why did the Greek city states feared democracy?

The greek city states did not fear democracy. They invented it.

Around 600B.C. before democracy was invented, the city-states had kings or nobles who run the affairs. When though, philosophers came up with the idea that the state would be run more effficiently with a type of government that included the people in decision-making, this was beyond any reason.

After 100 years though is was obvious to everyone that this new system of government, were the citizens of a town had power, was called Democracy (=demokratia), which is a made up-Word of demos-state and kratw-hold/power. It would freely translate in English as: People (state) holds power.

yes they invented democracy but the Spartians from Sparta feared democracy