Does it have to be philosophy?  Why not approach it from Evolutionary Psychology.  His ideal city would fail for the same reason that all utopian societies fail.  Humans are simply not constructed that way.

Of course, if you must go philosophical, the tripartite soul is a pretty good place to start.  Apetite, spirit, and reason supposedly correspond to productive, protective, and governing elements of society.  Why?  Has this really been epistemologically established?

Anyway... returning to evo pscyh, the fact is that humans are not divided into castes biologically.  There is no inherent gene for benevolent rulership, nor is there any way to effectively evaluate people based on divisions into such broadly generalized categories.  Digging ditches is always going to suck compared to attending state dinners.  One thing that is built into the human psyche is the desire to be top dog.  Competition is one of the key elements of natural selection, and this is reflected in our natures.  It can be no other way, if you think about it.  If natural selection happened upon an organism that didn't want to compete... well... it would die out.  Duh.

Where a lot of people make a mistake is in observing what appear to be acts of social altruism.  That is, some people "sacrifice all" for the good of the group.  This has been a thorn in the side of individual selection for a long time, but with the added support from Game Theory, we now know why it works.  People (or any organisms, for that matter) don't sacrifice for the group because the group would be better off.  They do it because on balance that kind of behavior comes out better for the individual!

It sounds contradictory, but it's not.

Consider a colony of birds in which only males who build and protect nests are chosen as mates.  There are less nesting spots than males, so typically, the strongest males build nests, leaving the weakest without mates.  We would expect that these males would fight with every ounce of strength to try to dislodge a nested bird so that they might mate and their genes survive, but this is not what happens.  They sullenly slink off to the edges of their territory and sit stoically while the nested males get about their business with the females.

For a long time, this was considered proof of group selection.  These birds were accepting their place in bird society for the betterment of bird society.  The thing is, that's not what's happening.  With continued observation, we see something new happen.  Birds that are nested and protecting eggs are more likely to hesitate when fleeing than those without nests.  They are also more likely to try to defend the nest against predators.  That is, unnested birds have nothing to stick around for, so they take to the air the instant a predator approaches.  Nested birds, on the other hand, owe it to their genes to stand and fight.  So, when the fox comes around, it's actually more likely that he will grab a nested bird than an unnested one.

What  happens after a nested bird has been killed?  There's a big fight between unnested birds to determine who gets the free nest.

Now, consider:  If an unnested bird were to try to fight a nested bird in single combat, what would likely happen?  He'd lose, of course.  That's why he's on the outskirts to begin with.  So not only would he lose, but he'd have that much less energy.  Supposing a nested bird dies, the unnested one that fought excessively is likely to lose the fight between the other unnested birds and continue to be unnested.  However, the ones who "stoically accept their place in the world" are saving their energy.  If they happen to be one of the best of the rest, they stand a better chance of mating from not fighting.

It's the same in humans.  People don't accept poverty or a life of menial labor.  It's just the best they can get at this time.  Instinctively, we all know this is true.  Any society in which people are assigned to roles will fail precisely because some roles will be better than others, and those on the outside will always want to get on the inside.  When caste societies work, it's not because the lower castes are happy with their fate as the footstool of civilization.  It's that they don't have any choice.

Slavery, forced servitude, etc, without hope of improvement cause depression in humans.  (Other animals too!)  It's just the nature of the beast.  Pecking orders are in our nature, and they are worked out through individual competition, not group selection.

If you have time, I'd suggest that you read "Nonzero" by Robert Wright.  It explains why group selection just doesn't work.  You can also learn a lot from "The Origins of Virtue" by Matt Ridley.  Between these two books, you should have enough evo psych information to be able to thoroughly refute the idea of ANY utopian society, not just Socrates'.

Thank you SO much, Hambydammit! That was very helpful. I was actually thinking of the same things, but you worded it and fleshed it out very well.

I'm assuming your taking this from Platos - Republic? If you still need help after friday I will come back and help, I'm currently writing a report over The Social Contract. Good luck!

You could say it would fail because God doesn't take no shit and Socrates pissed him off. His city actually existed as Jericho and God decided to preform an ethnic cleansing and completely erased it from history so we will never know of it.

 It was an offhand comment, KB.  I enjoy going to dinner much more than digging ditches.  I like having powerful friends, which is something state dinners are conducive towards.  The broad point is that people pretty much universally would rather have cushy non-strenuous jobs with comparatively high return than very difficult jobs with comparatively little return.  The nastiest jobs tend to be those that require very little specialized knowledge or training, which makes them inherently less valuable.  Your average mental midget can be taught to use a shovel.  Practicing real estate law (a cushy job if ever there was one) requires a lot of intelligence and training.

Yeah, yeah.  I know the argument... value is assigned, not inherent, but human nature is assigned -- by genes.  That's why division of labor always happens.