Maybe I should do a semi-full treatment of the Republic. Plato was way smarter than anyone writing in modern times. It's a net gain even though he was so often wrong.
The Republic is Plato's. There is little of Socrates in there, except insofar as he was obviously one of Plato's influences. Socrates did fall for the universalizing pathology.
However, having reviewed the topic in more detail: damn, all of Western thought really is footnotes to Plato, isn't it? Rather than Western or Christian, I may have to start calling it Platonic civilization; which is exactly its problem. Q: how is Plato still so influential? A: no one stops.
Epistemology is gender-neutral. The correct way to investigate a puzzle does not depend upon your plumbing. Truth is gender-neutral. Accurate beliefs are accurate regardless of who is believing them. As a result, from a philosopher's perspective, men and women are identical, and should act identically. Virtue is virtue. Did you catch the error? I skipped something important...
Philosopher: "The unexamined life is not worth living." Is that so? Plumber: "Good plumbing is vital. You will literally die unless you let me rip out all your pipes for replacements and let me bill you." Mere self-serving propaganda dressed up as profundity.
Socrates was accused of impiety because Athens was impious. His genuine crime was being too pious. ["Corrupting" the youth] was a result of Socrates attempting to instill some of his genuine piety into the young folk around him. Of course the corrupt are the first in line to call their opposites corrupt.
Athens was Fascist; they were impious in exactly the way America is impious. In today's America they don't have a corrupting the youth charge, so instead they will find a way to call your devotion "cultlike" if you dare have nonzero devotion to anything. Exception: you can be devoted to personal aggrandizement if you want. Have a cult of personality if that personality is yourself? Very okay.
Plato a feminist? Sounds plausible. He was a sodomite, after all. He had an interest in other men treating him like a woman, meaning he had a vested interest in making men seem womanly or vice-versa...
By the way, fun fact: justice is very very simple. It is when cooperators are rewarded and defectors are punished. Injustice is when cooperators are punished for trying to discourage defectors, and defectors' ill-gotten gains are defended. (You are here.)
Of course defectors will almost always present themselves as cooperators, so perhaps a dictionary of these types of camouflage would be handy, but the topic itself is very very far from deserving a book-length treatise.
Someone trying to make justice complicated is a criminal. They want to justify their crime so you forget to defend yourself. Or, ideally, you actively attack your own impulse for self-defence, thus making their life easy.
The crazed man asking for his sword is obviously going to defect with it, which is why Plato decides he shouldn't get it. Though also you ought to bring up this debt as he becomes crazy, rather than waiting for the very foreseeable crisis. Also also, not really a thing that happens, unless you're also going to mention, "But sometimes rich men can't pay their debts because they get struck by lightning and die," as if this were significant. E.g. if by 'crazed' we mean Alzheimer's, they will forget the debt even exists. This trash takes itself out.
It is not unimportant to remember that Socrates lived in a society that, while Fascist, was still differed greatly from the present. Socrates was tried by the Assembly; he was a member. There were only about 6000 total members. You could easily know all of them, at least to the point of fitting a name to a reputation.
Moreover, their hangout, the Forum, would be frequented by (get this) Forum regulars, of which Socrates was one. Everyone knows the regulars. Like a web forum, you could walk up to anyone in the Forum and strike up a conversation. By contrast, the "public" spaces in a modern city are filled with total strangers who will, as the saying goes, barely give you the time of day. (I have been asked for the time twice.) It's a minor miracle any of them even speak your language.
Basically Socrates was a Beltway pundit who decided to troll the other Beltway bureaucrats, only it was even more personal than that, because there's one or two more than 6000 Beltway bureaucrats. Unlike Congress, the Assembly was a genuine legislative body. Guess what happens when you aggressively troll the legislative body?