The Old Man becomes a symbol of the countless civilian victims of war-- those "without politics." The Old Man is going to die at the bridge--displaced, disoriented, alone. He's not a cat, nor a dove, but a goat--who was "only taking care of animals." When the Old Man said the above statement, he meant that he has no political role to play in the War. He meant that he doesn't support any side in the war and does not want to have participation in War.
Hope this helped :)