What does John Proctor say keeps him 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.