Why did Reverend Hale leave the court in Act 3 of The Crucible?

In act three, John Proctor brings Mary Warren to Salem's court and encourages her to testify that the girls are frauds. Proctor also brings a signed petition from numerous community members acknowledging that Rebecca Nurse, Elizabeth Proctor, and Martha Corey are morally-upright individuals. Giles Corey also attempts to share a signed deposition with the court accusing Thomas Putnam of using the witch trials as a land grab. Unfortunately, Giles Corey is arrested for contempt of court and John Proctor is silenced by Deputy Governor Danforth, Judge Hathorne, and Reverend Parris.

Reverend Hale is astonished that the court officials perceive every piece of evidence presented as an attempt to undermine their authority and realizes that Salem's authority figures are willing to harm innocent citizens in order to retain their exalted positions. After John Proctor ruins his reputation by confessing that he had an affair with Abigail Williams, Elizabeth lies to the court officials in an attempt to save her husband's reputation and John Proctor is arrested. Reverend Hale immediately denounces the court's proceedings and quits the court because he knows that it is corrupt. Reverend Hale mentions that he was always suspicious of Abigail Williams and believes John Proctor's testimony. Reverend Hale is filled with regret for previously supporting Salem's court and spends the rest of the play encouraging imprisoned citizens to offer false confessions in order to save their lives.

At the end of Act III of The Crucible Reverend Hale quits the court.  This action surprises the audience and shows us the changes that have occurred in his character.

I denounce these proceedings, I quit this court!

When Hale came to Salem in Act I, he came thinking he was coming to save the town, and its children, from a terrible witch outbreak.  As he says in Act IV "I came into this village like a bridegroom to his beloved, bearing gifts of high religion..."  Hale comes with his knowledge about the supernatural world, but without thinking the girls may be lying.

By Act III, the trail has taken over the town.  Highly respectable women are accused (Rebecca, Martha, and Elizabeth).  When Proctor comes to the court with proof (a signed deposition and Mary Warren's testimony) Hale is horrified that the courts will not let him present his case with a lawyer.

In God's name sir, stop here; send him home and let him come again with a lawyer-

Hale realizes that the courts are not interested in the truth.  They want to believe the trails are true and that the girls are not lying.  If they change their minds now, they'll be admitting they're wrong and have wrongly convicted innocent people.

When he realizes that the courts are not fair; he quits the court.

In The Crucible's Act 4, what happens to Reverend Hale after the Salem witch trials?

After initially supporting the Salem court and attempting to discover witches throughout the community, Reverend Hale experiences a dramatic change of heart in Act Three. In Act Three, Reverend Hale realizes that Danforth, Judge Hathorne, and Reverend Parris are corrupt officials, who are only interested in protecting their positions of authority. He ends up supporting John Proctor, Francis Nurse, and Giles Corey and denounces the proceedings after Proctor is arrested and charged with witchcraft. After quitting the court, Reverend Hale attempts to redeem himself by persuading innocent citizens to offer false confessions in order to save their lives. Tragically, he cannot persuade John Proctor into offering a false confession and fails to convince Danforth to postpone the executions. In his final attempt to save John's life, Hale begs Elizabeth to persuade her husband to change his mind. However, Elizabeth refuses to intervene and allows her husband to die a martyr. The play concludes with a final drum roll as Proctor is led to the gallows.

While Arthur Miller ends the play without elaborating on Reverend Hale's future, historical records reveal that Hale quit the court shortly after accusations were levied against his wife, Sarah, who was never officially charged or arrested. A few years after the witch trials, Sarah passed away and Reverend Hale wrote a book about the events that transpired in Salem entitled A Modest Inquiry into the Nature of Witchcraft.