The belief that Socrares “failed” because he was sentenced to death at the trial is a common misconception amongst those who are unfamiliar with the other dialogues, which is why I don’t think it’s the best one to start with. Plato explains in another dialouge, Phaedo, that Socrates does not fear death, and is in fact, more than willing to die for a just cause. In a way, Socrates got exactly what he wanted, because he died doing what he loved, which some would say is the best way to die. He even became a Martyr for it in the process.

Of course, Socrates wanted to live, but not for himself. He wanted to live for the sake of Athens. He remarks (paraphrased) “killing me will hurt you more than it hurts me,” because essentially it will. He thought that Athens still had much yet to learn, and so killing him would be one of their greatest mistakes.

He makes a lot of witty remarks, even some which might be considered sarcastic, but he doesn’t flat-out lie anywhere within the dialogue. He’a more annoyed than anything else because he believes he is innocent, and so he is somewhat frustrated that the trial is even happening.