Proctor had to make a decision about whether or not to confess, and in that decision he had to address the fundamental nature of his character.
This is a quote from a man named Tom Wilkinson, who played the part of Proctor in a production of the play. Wilkinson is referring to the insistence that Procter confess, and the choice he has to make about what kind of person he is. Proctor refuses to confess what they want him to, that he made a deal with the Devil. He does not want to give up his name because he says it is all he has left. He is willing to go to his death, but he refers to be part of the witch hunt (literally) and give legitimacy to the trial.
Proctor: You will not use me! I am no Sarah Good or Tituba, I am John Proctor! You will not use me! It is no part of salvation that you should use me! (Act 4, Scene 4)
To Proctor, this is madness: a group of girls starts accusing people of witchcraft, and soon dozens of people are put to death on the thinnest, obviously manufactured, evidence. He has accepted his fate, but he wants to go down with his pride. He will not let them take that from him.
Elizabeth wants John to confess because, as she says, then he could live. She ultimately tells John that it is up to him. He could not live with himself if he admitted a lie. He will not justify the nonsense. Other local towns shut down their courts when they came to their senses, but Salem held on. Proctor insists, rightly so, that the court is nothing but a place to nurse grievances and exact vengeance on one’s neighbors.
Miller clearly was making a political statement with this play, and particularly with Proctor. In a village of people who seem to have lost their minds in the witchcraft hysteria, Proctor maintains his sanity. He tries to protect the vulnerable. Proctor is a man of principles, and while he admits that he did something wrong in having an affair, he will not admit to consorting with the Devil because he didn't, and the entire situation is wrong.