"You still have a family that loves you," Zuko reminds her. Even without her mother, she still has her dad, grandmother, and Sokka. He then looks away again, but doesn't pull back his hand. He doesn't need to tell Katara about his family. After all, he has proof of his father's 'love' on his face.

"I've only ever felt close to my mother and my Uncle."

The first being gone, but... his Uncle. His Uncle who was more of a father to him than his actual father. He was lucky to have him on his side, and even in this place.