The Things They Carried doesn't really follow the classical narrative structure or the structure. While we do get exposition at the very beginning of the story in "The Things They Carried," when we're introduced to each character by the individual things that they carry, and to the war by the things that they all carry, the book sharply diverges from the classic plot structure from there on.
Throughout the book, we alternate seemingly randomly between conflict (Ted Lavender's dead!) and peace (Hey, a cute puppy!), and then back again (Azar blows the puppy up). At the end, nothing is solved. There is no real resolution. O'Brien is trying bring memories back to life with stories. O'Brien does this because he's following his own rules for writing true war stories. True war stories, O'Brien says, don't make sense in the way a classic narrative makes sense.
You know how you watch a romantic comedy or an action movie, and it's great, and the ending is satisfying – the guy gets the girl, or the guy gets the girl and blows up the bad guy, or some similar situation – but a small part of you knows it's fake, and feels cheated? It's because endings like that don't happen in real life. O'Brien's fighting against that Hollywood-ized, theatrical idea of war. He wants to write a true war story, something that could happen in real life, and that means he has to ignore the classic way of writing stories.