Gene makes this observation in Chapter 7:
The war would be deadly all right. But I was used to finding something deadly in things that attracted me; there was always something deadly lurking in anything I wanted, anything I loved. And if it wasn't there, as for example with Phineas, then I put it there myself.
This insight comes from Gene the adult narrator, not Gene the boy at Devon. In this passage, Gene recognizes and acknowledges that at the time he was at school, he was both insecure and self-destructive. Never at peace with himself, Gene existed in a perpetual state of conflict with the world around him and those in it. He defined himself through conflict and competition; only by "winning" did he feel any relief from his own self-contempt.
In Finny's goodness and open friendship, Gene found nothing to pit himself against; consequently, he manufactured competition and conflict, which was completely one-sided, of course, existing only in his own mind. Gene created the psychological scenario that Finny felt jealous of him, that Finny was sabotaging his grades, that Finny was secretly maneuvering to spoil whatever success Gene could eek out for himself at Devon. Once he had established this "straw man," Gene then went about "proving" himself--to himself, keeping his world intact.
When Gene grasped the truth that Finny did not harbor a secret agenda and had never meant Gene harm, he was psychologically shaken beyond endurance:
Any fear I had ever had of the tree was nothing beside this. It wasn't my neck, but my understanding which was menaced. He had never been jealous of me for a second. Now I knew that there never was and never could have been any rivalry between us. I was not of the same quality as he. I couldn't stand this.
It was within minutes of this realization that Gene "jounced" the limb throwing Finny to the ground, an act of aggression and violence born of Gene's sense of worthlessness.