What I find striking is that Thrasymachus just kind of rage-quits, yet his position wasn’t truly defeated; he simply abandoned the conversation. It makes you wonder whether "might makes right" rests on firmer ground than it first appears in the book. And of course, for Plato, someone who takes such a point of view had to appear as driven more by anger than by reason. — Zebeden

That's right. But Thrasymachus's psychological withdrawal sets the scene for the rest of the book, which is meant to defeat cynical nihilism philosophically, in a different way from that attempted in Book I—since direct refutation according to Thrasymachus's terms is shown not to be conclusive or persuasive.