The tree scene is one of the most important events in A Separate Peace and comes about when the boys, as part of their secret tree jumping routine, decide to do a double-jump together. Finny and Gene climb up together, and Finny moves out onto the branch first. Gene stays back, and with his hand still on the trunk, "jounce[s] the branch. As the branch falters, Finny glances back at Gene briefly while all of this is happening, like he is trying to figure out why Gene wiggled the branch, and then he falls to the ground with a terrible thud.
The most important aspect of this scene to consider is, of course, Gene's motivations for jiggling the branch under Finny. Gene's guilt will slowly eat away at him for the rest of the novel. Before the accident, Gene was just so sure that Finny was out to get him, trying to distract him from his studies, so he could ruin Gene's chances to be the top student. Then, when Finny comments that he did not realize that Gene needed to study and thought that grades just came easy for him, Gene realizes that Finny was not trying to undermine his studies after all. Most readers would think this insight would cause Gene to lighten up, but he becomes even more jealous over Finny's innate goodness. When they start climbing the tree, Gene's conflict, jealousy, and resentment are in turmoil, and he spitefully jounced the branch, causing Finny to fall.