Elihu had been listening to the entire conversation. It seems he couldn’t stand it any longer: he was angry with Job for what he said, and angry with Job’s three friends for their inability to answer Job.
Job 34:17 Could God govern if he hated justice? Are you going to condemn the almighty judge?
Even if Job hadn’t sinned before, Elihu’s view was that God was so righteous, Job had at least sinned by refusing to admit he might have sinned!
Job 34:35-37 Job speaks out of ignorance; his words lack insight. Job, you deserve the maximum penalty for the wicked way you have talked. For you have added rebellion to your sin; you show no respect, and you speak many angry words against God.