She doesn't deserve him. She never has and she never will. Katniss Everdeen, winner of the 74th Annual Hunger Games, deserved her victory. She was the strongest, the bravest, the best. Her crown was earned through her own virtue. But kindness has never been one of her virtues, neither has patience. At least not with people. Out in the forest, in her element, she can wait for hours. Poised and ready for the kill. Katniss could stay like that forever if she had to.
With people, it's different. When she hunts, she doesn't owe nature anything. You only take what you need and you move on. You spend a few minutes talking to a person and the next thing you know, you owe them. Whether it's for giving you information, or helping you with something, or giving you something, owing someone is never good. Owing leads to a cycle of paying and repaying; it's a waste of time and risky to boot. Let anybody in, and you run the chance of entering a terrifying state: reliance. In Katniss's experience, the only person she can rely on is herself.
That's not true, and she knows it. She may only want to rely on herself, but there is one person she can always rely on. The same person that she'll never quit owing. Peeta.
She knows that Peeta deserves someone softer, someone with a heart less barricaded. Peeta insists that she's perfect for him and that he'd never want anyone else and Katniss doesn't argue. She's painfully aware of her flaws, the things that should make her completely incompatible with him, but love has no rhyme or reason so she doesn't try to understand.
He deserves better, she deserves worse, but they need each other. Peeta's devotion almost shocks Katniss. Sometimes she still can't believe he's hers. He is too perfect for someone as abrasive as her. She feels corrosive in comparison, like one day she will wear away his sensitivity and he'll be the kind of person she is. Harsh. Cold. Broken in some ways, stronger than ever in others. But somehow, he never changes. He loves her. She loves him back. Love isn't what Katniss expected, but it is what she needs. She's aware of this. Just as strongly as she's aware she'll never deserve Peeta. Like with the Games, she can never forget. Unlike with the Games, she never wants to.