In "The Crucible" why do Parris and Hale want John to confess to witchcraft?
Reverend Parris is concerned because of the reputation of the people who are scheduled to hang in Act Four. He tells Judge Hathorne,
. . . it were another sort that hanged till now. Rebecca Nurse is no Bridget that lived three year with Bishop before she married him. John Proctor is not Isaac Ward that drank his family to ruin.
Rebecca and John are both well-respected, unlike many of those who were convicted before now, and this makes Parris fearful that people in the town will turn on the court, as well as him, if these hangings go on. He begs the judges for the executions to be postponed. He recalls that very few individuals came to Proctor's excommunication from church, and this speaks to the town's discontentment with Proctor's conviction and sentence. If John confesses, however, then it will seem to legitimize all of the convictions that have taken place so far.
Reverend Hale wants John to confess because he believes that "life is God's most precious gift; no principle, however glorious, may justify the taking of it." He feels that God will damn a liar "less than he that throws his life away for pride." Hale thinks that John's life is too big a price to pay to protect his pride. He would rather see John tell a lie by confessing and live, than to retain his pride, keep silent, and die.
Further, Hale feels incredibly guilty about his role in the trials. He cries, "There is blood on my head!" because he feels partially responsible for the deaths that have already taken place. If he can persuade John to confess, saving his life, then this is one fewer death that will rest heavily on his conscience. However, I think his concern for John and his soul does outweigh Hale's concern for himself and his guilt.
The answer to this one can be found in the beginning of Act four. At the beginning of this act, several highly reputable people are set to hang: Rebecca Nurse, Martha Corey, and John Proctor. These are people that the townsfolk respect and look up to, who were well-liked and had influence in the town. Parris is worried that if they hang, the townspeople will rebel and overthrow the courts. He has already seen the town turning against him; he found a knife stuck in his door that morning, and Abby had just skipped town. Things aren't looking good for him. He is worried that the townspeople will finally be fed up with the hangings and stage a rebellion, which might be dangerous to him. So, Parris thinks that if Proctor will confess, maybe that will set an example for the others, and they will all confess. If they do confess, they won't hang, and maybe the townspeople won't get so angry, and he will be safe.
Hale wants Proctor to confess for different reasons; he doesn't care if the townsfolk rebel. In fact, he wishes it would happen. Hale has been striving with all of the accused, trying to convince them to confess in order to save their lives. As he puts it to Elizabeth Proctor, God damns a liar less than one who will die for pride. Hale simply wants people to stop getting hanged. He feels responsible for their deaths, and is trying to keep people from hanging because they won't confess. He feels that if Proctor confesses, his life will be saved, and maybe that will convince the others to confess and save their lives too.
I hope that those thoughts help; good luck!