John Proctor's reason for not going to court is understandable, but selfish. He knows in approaching the court with Abby's lies, he may expose his own affair, which will ruin his good name. As a result, innocent people will be charged and some will die.
He is covering for his good name in the community. Early on Abby reveals that it is all farce. However, it is revealed that Proctor has had an affair with Abby, and given the strict Puritan code of conduct and public shame, this complicates things drastically. If he exposed the girls as frauds, it means he must confess his adultery, which is a grave offense.
So it save his good name, he keeps quiet and hopes things will blow over. This, of course, adds to the irony of the play. Had Proctor spoken out, innocent lives likely would have been spared but his name would have been shamed. Since he keeps quiet, many innocent people are murdered and his name is shamed, but through his refusal to have his confession tacked on the church door, he recovers some of his dignity, albeit it costs him his life.
JOHN PROCTOR DOESNT EXPOSE ABGIALS LIE BECAUSE HE DOESNT WANT THE PART ABOUT HIM SLEEPING WITH HER TO COME OUT>