You can argue that what drives Jake is the desire to prove he is still a man despite the wartime injury which has left him impotent. The first way he does this is by what Hemingway called 'grace under pressure'; he never moans about it to his friends, the only time it comes up is with Brett, when the lovers have to accept they can't actually make love. Thus Jake maintains a manly dignity.
Secondly, Jake maintains his interest in typically manly pursuits. His pleasure in the fishing trip with Bill Gorton is evident from Hemingway's crisp prose. Unfortunately, Bill catches bigger fish than Jake, but there is no indication that Jake feels undermined as a fisherman or a man.
This brings me to my final point to do with Jake's meticulous preparation of the fish he has caught, 'I .... washed them in the cold, smoothly heavy water....packed them....on a layer of ferns...and I put...(them)..in the shade of a tree.' Such naturalistic imagery marks that Jake still needs to feel a part of the natural World around him. This I suggest, is even more important than still being a man.