The old man is symbolic of the devastating effects of war on civilians who have nothing to gain from the conflict.
When the narrator meets him, the old man is simply "too tired to go any farther," and he never wanted to leave his home to begin with. His primary concern was in taking care of animals, which represent the innocent. Now this man, whose life has been devoted to caretaking, is being forced to flee his home because of forces of destruction. Because of this war, he has had to relinquish all he holds dear: his home, his animals, and his sense of belonging.
The old man is emotionally depleted. He is "without politics" in this war and has nowhere to go if he can make it off this bridge. Finally, the narrator successfully urges him to try to move forward, but after a few wobbly steps, the old man is forced to sit down in the dust again.
The narrator comes to understand that "there was nothing to do about" the old man, and in this realization, he also understands that the old man will die at this bridge. Displaced, alone, and dejected, the old man no longer has his animals and faces "enemy" forces whose battles are not his own.
The symbolism of the old man shows the devastating impacts upon those who are surrounded by war and have no voice in either the circumstances or the outcome of the battles around them.