Thrasymachus is a professional rhetorician; he teaches the art of persuasion. Furthermore, he is a Sophist (he teaches, for a fee, men to win arguments, whether or not the methods employed be valid or logical or to the point of the argument). The ancient Greeks seem to have distrusted the Sophists for their teaching dishonest and specious methods of winning arguments at any cost, and in this dialogue, Thrasymachus seems to exemplify the very sophistry he embraces.
It is clear, from the outset of their conversation, that Socrates and Thrasymachus share a mutual dislike for one another and that the dialogue is likely at any time to degenerate into a petty quarrel. Both speakers employ verbal irony upon one another (they say the opposite of what they mean); both men occasionally smilingly insult one another. At one point, Thrasymachus employs an epithet (he calls Socrates a fool); Thrasymachus in another instance uses a rhetorical question meant to demean Socrates, asking him whether he has a bad nurse who permits Socrates to go sniveling through serious arguments.
Thrasymachus opens his whole argument by pretending to be indignant at Socrates' rhetorical questions he has asked of Polemarchus (Socrates' series of analogies). Socrates, no innocent to rhetoric and the ploys of Sophists, pretends to be frightened after Thrasymachus attacks by pretending to be indignant. So Thrasymachus acts like he is infuriated, for effect, and Socrates acts like he is frightened — for effect. When Socrates validly points out that Thrasymachus has contradicted himself regarding a ruler's fallibility, Thrasymachus, using an epithet, says that Socrates argues like an informer (a spy who talks out of both sides of his mouth). The point of this is that none of it advances the logical or well-reasoned course of the discussion.
