Why does Hale denounce the proceedings in The Crucible?
Hale denounces the proceedings because it is clear that the girls are not telling the truth in their testimony.
To denounce something is to explain why you disagree with it.
It is during the questioning of Mary Warren’s and Elizabeth that Reverend Hale becomes suspicious and officially jumps off the witchcraft bandwagon. Mary Warren is supposed to have found a needle left in the doll by Abigail.
Hale: Mary - you charge a cold and cruel murder on Abigail.
Mary Warren: Murder! I charge no -
Hale: Abigail were stabbed tonight; a needle were found stuck into her belly -
Elizabeth: And she charges me? (Act 2, Scene 2)
Elizabeth says that Abigail is murder, and should be ripped from the world. Of course, Elizabeth has a reason for not wanting Abigail around since the girl had an affair with her husband. It is all too convenient. Reverend Hale is not convinced. He realizes that the whole of the doll and the needle falls apart and that Mary Warren is not reliable. She is just a girl caught up in the hysteria. Elizabeth is a woman with an ulterior motive. Reverend Hale gets annoyed, and has had enough.
Hale: Proctor, I cannot think God be provoked so grandly by such a petty cause. The jails are packed - our greatest judges sit in Salem now - and hangin’s promised. Man, we must look to cause proportionate. (Act 2, Scene 2)
Hale has come to the sensible conclusion, deciding that the whole thing is ridiculous. There is no witchcraft, there never was any. They are all getting excited over nothing. Abigail is pretending, Mary Warren is confused or pretending, and Elizabeth is petty and jealous. In the end, they are only hurting themselves with the witch hunt. They are tearing their community apart. That is why he denounces the proceedings thusly with this.