Reverend Hale changes his position on the witch trials because he is determined to save John Proctor from execution. He becomes convinced that Abigail Williams is a liar in Act III, after she is asked to respond to the confession of John Proctor to lechery.
Proctor admits to a crime, lechery in the court, a serious crime, this gets Reverend Hale's attention, he considers what would cause a man to confess to such a crime in front of the high court. It must be true, that is the only answer.
Abigail is defiant in her non-response to Danforth, refusing to reply to the question. Hale proclaims that he believes Proctor.
"I believe him! Pointing at Abigail: This girl has always struck me as false"
Hale becomes convinced that the court does not care about the truth, a man has just surrendered himself to the crime of lechery and they do not believe him, they would rather charge him with witchcraft.
Reverend Hale can no longer be a part of this charade that ignores the truth and elevates a liar, Abigail Williams.