As he started to leave, Katara opened her mouth to apologize. Anything to keep him from going. As it turned out, though, she didn't have to. He stopped on his own.
With a soft sigh, she rose to her feet. "It's a part of who you are, Zuko, it isn't all of who you are," she stated simply, hands resting on the back of her chair as she faced him. "You find a way to get by and you do it, until we can fix the problem. You keep helping people. You keep living. I'm not saying it's easy, but I am saying you're about more than just firebending. It's time you realized that."
Her voice wasn't sharp. It wasn't attacking. She was just stating what she considered to be facts. While Katara understood he was physically drained, she also knew that a good bit of this was him stuck on his lack of being able to bend. Getting over that, she thought, would help Zuko a great deal.