Thrasymachus, true to his name, breaches the perimeter of the dialogue with all the abandon of some sort of comic glorious soldier (miles gloriosus), and Socrates gleefully skewers this rash fighter. As noted elsewhere in the commentaries, we do not (and the Greeks did not) intend to denigrate the fine art of classical rhetoric (method of persuasion in argument); rather, it is necessary that we identify and refutespecious rhetoric. And in this dialogue, Thrasymachus plainly shows himself to be a sophist, a specious rhetorician. His is a common human malady: arrogance. Thrasymachus displays his character as a sophist in the entirety of his contribution to the debate. We have reviewed in the commentaries the specious nature of his rhetoric by noting his habit of name-calling (irrelevant to the argument), his self-contradiction (a fallacy in argument), his feigned indignation (an empty rhetorical ploy, irrelevant to the argument); indeed, we might summarize a formidable list of the fallacies in argument for which he is culpable. His argumentvis-à-vis the question of rarifying the question of justice is, we remember, that might finally makes right, in which case, logically, he is confuting two things: right and might. We remember, Socrates remembers, and Thrasymachus remembers — or so he says, after Socrates has argumentatively forced him to confess his having remembered.
As a sophist, Thrasymachus seems to serve as a kind of adversarial "straw-man" to Socrates' probing philosophy, but a fair analysis does show him to be a typical sophist. When we analyze his argument and his general way of comporting himself in debate, we can appreciate why the ancient Greeks so disdained the sophists. Thrasymachus ends his participation in the conversation by meanly congratulating Socrates on his "victory," and advising Socrates to "feast on his triumph" as though a supposed mutual effort at defining the philosophical question of justice were some sort of gladiatorial contest.