Like most of the stories, this story is narrated by Tim O'Brien. Throughout the story he tells us about the life of the man he killed. He adds intimate details like the man's feelings and relationships with his family. O'Brien imagines this man's life from every angle he narrates about the man's goals and dreams of going to college, how he is good at math, and an intellectual rather than a warrior. The narrator has no way of knowing all these details.
O'Brien generates a story from his imagination and his guilt. He feels guilty for killing the man,a man he didn't know. He knows the man must have had dreams, a family, people that loved him, conflicts, and everything else a normal human being has on every part of the planet. By telling his story O'Brien humanizes the man and makes him real. You get the feeling as he tells the story that the details come from his own past because he realizes the man he killed was a boy just like him, that could have even had a similar story. We know O'Brien didn't want to go to war in the first place but went anyways so that he didn't let down his family.