Why does Nat refuse the farmer's offer of a gun?
Nat is a realist. He is shown to be extremely perceptive about the world around him. He understands the magnitude of the challenges with the bird before anyone else. Contrary to the Triggs' denial, Nat understands the situation and possesses a sobering realism keeping a cool head in dealing with the intensity of what confronts him.
With this realism in mind, he rejects the farmer's offer of a gun. Nat understands that the gun is not going to be of much use. With the massing of the birds, Nat understands that a gun is going to be fairly useless. Even if he could get one or two shots off, he recognizes that the birds will continue to attack in forceful waves. Nat's realism compels him to reject the gun. He understands that the only way to confront the challenge of the birds to do so with as wide open focus and sense of realism as possible. There can be no "easy fix" such as the gun to resolve this situation. For the realistic and tough minded Nat, the gun is not going to help. It is for this reason that he rejects the farmer's offer of the gun.