Finny refuses to accept that there is a war because his injury prevents him from being able to participate. Of all characters, Finny would have been appropriately suited for war because of his athletic ability, however having his leg broken has created a long-term injury that will forever keep him from war. Externally, Finny doesn't let the other boys know that he has this feeling. Internally (readers later find out), Finny has been writing to different countries hoping for a way to be involved in the war.
Finny's denial demonstrates a truth of human nature. Those things we care about the most can consume us to the point that we will lie to ourselves or others.