It’s a basic philosophical argument that liberal democracy always leads to tyranny.
main ideas here are:
Unrestrained liberty and equality (the qualities of both Democracy and Anarchy) are corrupting, as is the unrestrained accumulation of wealth (the quality of Oligarchy). In respect to this conversation, what is true for a person, is true for the state.
A state run by those best suited to run it is more stable and effective than a state run by those who obtain power other ways (such as by wealth, or by merely being a citizen, such as with a democracy).
Each “higher order” form (Aristocracy, Timocracy, Oligarchy, etc) has a tendency to devolve into the next form in line (where Timocracy becomes Oligarchy, Oligarchy becomes Democracy, and Democracy becomes Tyranny).
A mixed Republic that places Aristocracy first, then Timocracy, and then under those Oligarchy and Democracy can help avoid the decent into Tyranny (while preserving the virtues of Oligarchy and Democracy and allowing those who naturally have a tendency toward those systems to exist and thrive within those sub-systems of the state freely).
Since Democracy is the form that the others devolve into before devolving into Tyranny, a central aspect of this theory is “How Democracy leads to Tyranny.”
Since Oligarchy specifically devolves into Democracy, a state ruled by Oligarchs is a slippery slope. In Plato’s book, a full chapter is devoted to showing us how an Oligarch is lifted up as the champion of the people, and how he over time becomes a tyrant.
Since Timocracy specifically devolves into Oligarchy, a state ruled by Timocrats is a slippery slope.
Thus, you either have a Monarchy/Aristocracy (rule by a wise one or few), a Mixed Republic (a mixed system), or a decent to Anarchy and then Tyranny (a decent toward chaos which results in a despot taking control).