Despite Gene's disbelief in the possibility of a 1944 Olympics, he agrees to establish a partnership with Finny and begin training for it. Why?

Gene loves Finny and Finny is excited about the prospect of training Gene. There is an unhealthy homo-erotic co-dependence thing going on here. Gene is attracted to Finny as well as feeling guilty about the accident. Agreeing to this sports partnership is a way to return things to "normal". Both boys seem able to swap parts of their identity to re-create a status-quo.