In A Separate Peace, Finny's falling from the tree is the pivotal moment in the novel. It is the catalyst for the plot, conflicts, themes, etc. It leads to the examination of illusions, friendships, loyalties, competitions, and the disintegration of all of the above.
The pivotal passage follows:
Holding firmly to the trunk, I took a step toward him, and then my knees bent and I jounced the limb. Finny, his balance gone, swung his head around to look at me for an instant with extreme interest, and then he tumbled sideways, broke through the little branches below and hit the bank with a sickening, unnatural thud. It was the first clumsy physical action I had ever seen him make. With unthinking sureness I moved out on the limb and jumped into the river, every trace of my fear of this forgotten.
With Finny turning to look at Gene with interest, the passage creates a particularly poignant scene. With the sickening, unnatural thud and Gene diving without fear, the passage showcases the hideous nature of what Gene does.
Finny comes to get Gene for a meeting of the Super Suicide Society of the Summer Session. Finny tells Gene that Leper (Elwin Lepellier) is attempting to qualify by jumping from the tree. Still thinking that Finny is trying to sabotage Gene by taking time away from his studies, he sarcastically concedes to go. Gene eventually realizes that Finny assumed academics came easily to him as sports came easily to Finny. Gene understands that Finny was never envious of Gene, at least to the point of trying to sabotage Gene's goal of becoming the best student. Finny tells Gene to study but Gene says he's done enough and they go to the river. At this point, it seems that Gene has relinquished any ill will he had with Finny and Gene has come to see that Finny was never planning to ruin his chances of becoming Valedictorian.
Gene and Finny climb the tree, planning to jump together. While climbing the limb, Gene "jounced" it, causing Finny to lose his balance and fall onto the bank, where he shattered his leg, making him unable to play sports ever again. It is not clear, even for Gene, if this was accidental, subconsciously on purpose, or both.