Ever the eager organizer, Brinker first suggests that he and Gene should enlist before Finny returns to Devon. That plan ends when Finny reappears on campus; life is changed, but the isolation from the war brought about by the school environment and by Finny's refusal to believe in the war allows Gene to gracefully avoid the whole topic.
Brinker assumes Gene is avoiding enlisting in some branch of the military because he feels sorry for Finny, who is ineligible for the military due to his injury.
You've been putting off enlisting in something for only one reason," he said at once. "You know that, don't you?" "No, I don't know that." "Well, I know, and I'll tell you what it is. It's Finny. You pity him."
Brinker goes on to express his belief that Finny is going to begin to pity himself if his friends and classmates don't stop "beating around the bush" about his condition. Gene refuses to accept, or even consider, Brinker's position, but also refuses to be drawn into any further consideration of enlisting at that time.