In The Crucible, why doesn't John Proctor immediately tell the court his knowledge?

In Act II of The Crucible, we see Proctor at war with himself when challenged by his wife Elizabeth to tell the court what Abigail told him earlier: namely, that the witchcraft allegations are unfounded. Proctor hesitates to tell the court the truth, because this would hurt Abigail, expose her as a liar, and at this stage he still has feelings for her, as Elizabeth realises:

She has an arrow in you yet, John Proctor, and you know it well! (Act II)

Proctor therefore struggles to do what he knows to be the right thing. He does go to the court eventually, but only after his own wife Elizabeth is arrested, and he still hesitates to confront the court too openly. It all ends in disaster for him as his own affair with Abigail is revealed, destroying his credibility in the eyes of the Puritan court officials, and he too is accused of witchcraft.

Therefore, Proctor's personal entanglement with Abigail proves to be his undoing and destroys his good name. Ultimately, the only way out for him is death, which he chooses rather than falsely confessing to witchcraft. This, at least goes some way to redeeming him in his own eyes, atoning for his sin of adultery and his earlier hesitation to condemn the fear and falsehood of the court:

Now I do think I see some shred of goodness in John Proctor. Not enough to weave a banner with, but white enough to keep it from such dogs.  (Act IV)

Why hasn't John revealed his knowledge to the court in The Crucible and what does Elizabeth believe is his reason?

Towards the beginning of act two, John Proctor is astonished to learn that Mary Warren is a revered official in Salem's court and there have already been fourteen arrests. Elizabeth also tells John that the judges hold Abigail Williams in high regard and he responds by calling the trials "black mischief." When Elizabeth encourages her husband to travel into Salem and testify that Abigail told him they were simply pretending, John hesitates and says that he will think on it. Elizabeth then gets up from the table and John says,

"I am only wondering how I may prove what she told me, Elizabeth. If the girl’s a saint now, I think it is not easy to prove she’s fraud, and the town gone so silly. She told it to me in a room alone - I have no proof for it" (Miller, 53).

Essentially, Abigail told John in private that she and the other girls were pretending while no one else was in the room to act as a second witness. John worries that his word will not hold up against Abigail's word in Salem's court because of her revered status. Given John's history with Abigail, Elizabeth immediately takes offense to the fact that he was alone in a room with her. Elizabeth attributes John's affection for Abigail as the reason why he refuses to tell the truth to Salem's judges when she asks her husband,

"John, if it were not Abigail that you must go to hurt, would you falter now? I think not" (Miller, 54).

What prevents John Proctor from telling the court what he knows in The Crucible?

When Proctor tells Elizabeth what he has heard from Abigail, Elizabeth insists that John go to the court to inform them of what he knows. 

At the time, Proctor hopes to stay out of the mess in town stirred up by Abigail and her friends and he says that soon everyone will realize the truth. Proctor hopes that they will see through Abigail's lies before they go through with any sentencing.

Proctor knows that the accusations the girls are making are fraudulent, but he fears that he cannot prove this as fact. Abigail directly tells Proctor in the opening scenes that there was no witchcraft involved in what the girls were doing in the woods.

He is not sure that he can prove what Abigail said to him. There are no witnesses...

The undercurrent of Proctor's refusal to tell the court what he knows is his former affair with Abigail. He does not want to be affiliated with her and could be afraid of being found out publicly. Ultimately this is what happens when Proctor has to tell the court what he knows in order to save Elizabeth.

He confesses everything at that point.