I assume that you are talking about the episode in Chapter 7 where Brinker brings Gene down to the Butt Room.
Brinker has been teasing Gene, saying that Gene has killed Finny in order to have a big dorm room all to himself. He brings Gene down to the Butt Room, saying they'll go smoke. But once they get to the room, Brinker tells the people there that he has brought a criminal and wants them to try Gene for "doing away with his roommate."
Gene is already feeling guilty because he made Finny fall of the tree so he sort of snaps when Brinker does this. He then realizes he's made a mistake. To maintain control of the situation, he tries to make a light-hearted false "confession." He says he put some arsenic in Finny's coffee. He tries to break the tension by pronouncing "contretemps" in the French way. He starts telling a crazy story about why he tried to kill Finny -- talking about catching Finny cheating on entrance exams and about how Gene made love to Finny's sister.
So basically he tries to maintain control by lightening the mood in the room with his "confession."