Prove that the old man is thefatalistic hero of the story

First let's define what it means to be fatalistic. Basically, fatalism is the belief that we have little control over future events. It is also the belief that we can do little to change what fate determines for us. So, a person who is fatalistic is a person who believes that he must resign himself to the inevitable.
In the story, the old man makes no move to continue on his journey, despite the narrator's warning that the enemy is approaching. While the narrator watches the bridge anxiously for the enemy's advance, the old man seems content to talk about his animals. He tells the narrator that he left his farm only because he was told to do so.
The old man divulges that he has no relatives and that the animals he left behind were his only family. He talks about the animals with love and great emotion. Although the narrator tells him that there are trucks up the road that will take him to Barcelona, the old man makes no effort to move in that direction; he proclaims that he knows no one in Barcelona.
At the end of the story, the narrator again urges the old man to move on. For his part, the old man stands up but appears too weak to make the journey to the trucks on foot. He sits back down and mumbles that he has only been taking care of his animals. So, the old man is fatalistic because he has resigned himself to whatever fate will befall him. He accepts that he can do nothing else to save himself, and his actions demonstrate his belief that it is futile to struggle against the inevitable.