At times through the course of A Separate Peace, Gene is completely content to be Finny's best friend and to follow wherever Finny leads; at other times, Gene feels insecure and competitive about the relationship. The difference in areas of ability between the two boys becomes the background for the conflict that shapes the story.
Finny is a naturally superior athlete - he doesn't need to work at being graceful or fast or strong or any of the characteristics he demonstrates effortlessly. Gene is the better student, by far, but he does need to study in order to maintain his grades. When Gene first becomes aware of this distinction, he immediately interprets it as being a competition, a conscious effort by Finny to distract him from his studies so that Finny can maintain his position of supremacy.
He had won and been proud to win the Galbraith football Trophy and the Contact Sport Award,...If I was head of the class on Graduation DAy and made a speech and won the Ne Plus Ultra Scholastic Achievement Citation, then we would both have come out on top, we would be even, that was all....He minded, despised the possibility that I might be the head of the school.
Later, the realization that Finny did not see the difference as a contest, that Gene was the insecure one misinterpreting the situation, drove Gene to unconsciously bounce the tree branch.