According to Plato, what was the biggest problem
in ancient Greek society?

Democracy

Explanation:

"Plato witnessed democracy begrudgingly in his city of Athens. Ancient Athenian democracy differs from the democracy that we are familiar with in the present day. Athens is a city-state, while today we are familiar with the primary unit of governance operating nationwide. Consequently, governance of a smaller population enabled more ‘direct’ forms of democracy rather than the ‘representative’ forms accorded by contemporary constitutions.

All citizens (with the pertinent qualification of their being free men) were permitted the opportunity of equal political participation: Important decisions were made by the assembly, where each citizen had the right to speak and the majority of offices were assigned by lot.

Professional prosecutors and judges did not exist in Ancient Athens. Instead, it was left to the ordinary citizen to bring indictments, act as jurors, and deliberate on the outcome of trials."

Plato argues that philosopher kings should be the rulers, as all philosophers aim to discover the ideal polis. The 'kallipolis', or the beautiful city, is a just city where political rule depends on knowledge, which philosopher kings possess, and not power.

Explanation:

His writings explored justice, beauty and equality, and also contained discussions in aesthetics, political philosophy, theology, cosmology, epistemology and the philosophy of language. Plato founded the Academy in Athens, one of the first institutions of higher learning in the Western world.