In "A Separate Peace" by John Knowles, why does Finny make up the story about "the fat old men"?

The war is a supremely important and serious event that everyone in Finny's life seems to be talking about. The entire world around him is focused on producing soldiers from his generation to fight in the war. However, Finny cannot fight due to his injured leg. As we know, Finny loves to be the center of attention, which is why he wears eccentric clothing and is always found in the center of the crowd. The war makes Finny feels left out due to his injury.

Finny wants to train Gene to compete in the 1944 Olympics. He tells Gene that since he (Finny) can no longer compete, Gene has to do it for him. In this way, Finny can live vicariously through Gene even with his (Finny's) injury. Having a war going on gets in the way of this plan. Gene wants to enlist in the war, which would separate him from Finny. So Finny makes up a story (which he himself believes and convinces Gene to believe) about the "fat old men" who are conspiring to fool the younger generation into thinking that there is a war, to stop the young people from having any fun. The lie about the "fat old men" serves as a way for Finny to keep Gene under his thumb, to keep Gene close to Finny, and to enable Gene to fulfill Finny's fantasy about competing in the Olympics. If Gene thought that the war was real, he would be much more likely to enlist. Therefore, believing that the war is fake keeps Gene from focusing on things other than Finny and their friendship.

Being the only two people who "know" about the "fat old men" draws Gene and Finny into a world of their own, where they can only trust each other. This brings them closer together.

Finny's vision of the fake war invalidates the commonly accepted world view. Within his dream of sending Gene to the Olympics, he creates a new reality to fill the void created by his (Finny's) disbelief of that world view. In this new reality, the war is fake, and can only drag on for so long. It will end before 1944, and Gene will be able to compete in the Olympics. The 1944 Olympics can occur only in a world where the war was fake. In this new reality that Finny created, his vision of living vicariously through Gene's athletic success could come true.

Finny's offer/demand to train Gene for the Olympics was an invite to a whole new world - a world where the war and wartime troubles did not exist. Ultimately, it is an invite into a new world where Gene could be more like Finny, just like Gene always wanted.