What does finny insist must have made gene bounce the branch that day?

The answer is blind impulse. This means the sudden and uncountable desire to do something. In the novel, Finny and gene have been each other's double from the beginning of the novel. Gene says to Finny the he would never have been good in the war, since he would have been willing to play basket ball with the foe instead of fighting.  This brought Finny in to tears, and asks if Gene's part in the fall was just "blind impulse" and not a deliberate expression of hate.