John Proctor has privately sinned, as he sees it, and he has privately performed penance. The weakness in his character that led to his affair with Abigail is in contrast to his public identity as a strong willed man. When Proctor has to go to the court to save his wife from false accusations of witchcraft, Proctor's private and public lives come into direct conflict.
In order to save Elizabeth, Proctor has to admit to his private mistakes with Abigail.
Proctor does not want to admit his failings as a human and a husband--I mean, there are small towns, and then there was Salem, Massachusetts. There's no recovering from that kind of confession. At the same time, people are dying because of a lie he knows about, so how can he allow that to happen because of his own pride and fear? It's a perfect dilemma with no easy way out.
The above post is correct; I would just add the bigger moral dilemma which prompts John Proctor to even consider confessing to a crime he did not commit. He believes he is a sinner who is unworthy of acceptance by God. He has a crisis of faith, and it is only when he is able to make his peace with God that Proctor is able to see that he has something worth dying for--his name, his integrity before God.
Isn't this the conflict about whether to confess and then have the confession signed and publicized?
He wants to confess and live, right? That's kind of personal -- he doesn't want his wife and kid to be alone after he dies. But at the same time, he doesn't want to lose his good name -- the respect that people have for him. This is his public self.
So his private self wants to live, but his public self doesn't want to pay the price necessary for allowing him to live.
The crucible act IV help
what is the conflict Proctor faces that puts his private and public self into conflict?
In Act 4 we find Proctor in jail on the day of his execution. The judges Danforth and Hathorne are desperate for Proctor to confess to being a witch. Some months have passed now since the start of the play. The hysteria has passed, but people are still in jail and have been executed. Abigail has vanished, stealing money, and public opinion is beginning to turn. Thus the desperate need for the confession – to prove that the process hasn’t been based on lies. This Act really emphasizes Proctor’s struggle with his identity. He is unable to make the confession and save his life because of his pride.
This has indepth info about Proctor throughout the play: