What is the climax in the novel A Separate Peace ?
The climax of John Knowles' A Separate Peace comes at the "trial" organized and presided over by Brinker.
This episode threatens to undo Gene's social position and to condemn him in front of the whole school for what he did to Finny. As the protagonist, Gene's fate is the most important issue in the text, though Finny's well-being is strongly linked to Gene's own conflicts. In this episode the fates and futures of Gene and Finny (and Leper and Brinker, too) are decided. Thus the stakes are highest in this moment of the story.
Also, the action that follows in the narrative does not continue to raise the stakes and does not create new conflicts or complications. When Finny breaks his leg again, the situation is actually simplified and his health can be seen as the denoument of the narrative (the resolution of the novel's conflicts relating to guilt and innocence).
When Brinker sets out to unearth the truth about how Finny fell from the tree and broke his leg, he says that it is in an effort to erase any mystery.
"We don't want any mysteries or stray rumors and suspicions left in the air at the end of the year, do we?"
This hunt for the truth places Gene on trial and leads to Finny and Leper both acting as witnesses. Leper and Finny both fail/refuse to divulge the answers Brinker is looking for and finally Finny gets up and leaves the room.
Everything after this point in the novel can be considered resolution as the high-point of the action and tension pass as Gene's public innocence is implicitly secured when Finny leaves without blaming Gene in front of the school.
When Finny, recuperating in bed from a re-broken leg, tells Gene that he does not hold Gene guilty privately, he is reinforcing a conclusion that has already been established in the trial scene.
"'I believe you. It's okay because I understand and I believe you. You've already shown me and I believe you.'"
Although Finny struggles to truly mean what he is saying, the nagging uncertainty of Gene's guilt/innocence is also established in the trial scene. Gene is not innocent entirely nor is he guilty of real malice. Instead, Gene is faced with the fact that he is flawed. His flaws do not, we should note, mean that he is morally beholden to the judgement of others like Brinker -- people who are flawed as well and subject also to moments of moral weakness and doubt.
Side-note: One way to identify the climax of a narrative is to look for the episode that brings the story's conflicts into resolution. In A Separate Peace the principle conflict is the complex question of Gene's guilt -- whether or not Gene will be found out by the entire school for injuring Finny, whether or not Finny can truly forgive Gene, and whether or not Gene can finally forgive himself and get over his guilt.
If you feel that, in this case, the conflict of Gene's guilt/innocence is not actually resolved until Finny says he believes Gene then you can argue that Finny's proclamation is the true climax of the story. Again, the argument presented above suggests that Gene's conflict (and that of other characters) is largely concluded when Finny abandons the trial.