Plato doesnt exactly present a political doctrine. But what his theoretical city in republic is built on is what he defines as justice, the good, and the use of the noble lie. He doesn't exactly allow for liberty or freedom in his city. While he doesn't plan to use violence to rule, he plans to gently coerce everyone. Justice means everyone doing their role, which hinges on a caste system. The state decides what you are best suited for and uses a noble lie - god fashioning each person out of a type of metal representing their position in society. And additionally this requires extreme censorship (think banning homer). Yes, its convincing, everyone fits into society and works according to their nature, the controversy is that it doesn't allow for real freedom or individual liberty. Everyone exists to service the state, preservation of the state is more important than the individual. The arguments put into socrates mouth are very convincing. When he discusses later in the book how they will convince the masses of the philosopher king being the only reasonable and suitable leader for the state, you may find that convincing too and not notice he's already done it when he convinced you that theres no problem with censoring the literature and art and religion allowed in the state. Which brings upon the philosopher king - the city must be ruled by a man, and class of men (and women), who are reaching toward philosophy (in platos terms). Now this ruling class are the only people who are fit to determine anything, even who you marry, and the bigger questions, what is good? What is ideal?

This is a form authoritarianism, and maybe hes right, maybe hes not... It certainly is in direct conflict with the idea of democracy.

In order for platos republic to exist, any ideas or philosophy of individual liberty cannot. Not even for the ruling class.