Zuko always found one thing hard to believe when he was with the Avatar's group.
His lack of title.
He was Prince Zuko. Not Zuko. Or Angry Boy. Or Angry Jerk. Prince Zuko. They just couldn't get it through their thick heads he was a Prince, not a peasant like them.
For all of his life, he had been Prince Zuko. A person people looked down on because of his father's feelings toward him. A person with no future.
Then he had become Banished Prince Zuko. His name was treated like a curse word around the Fire Nation. Not only did he not have a future, he was a disgrace. A failure.
But here, with the Avatar, he did not have a title. He was treated like one of them- sure, Sokka did get to be a problem with his disbelief that Zuko was good , but quickly lighting a nearby object on fire usually shut him up.
It felt good to be accepted, to be in a place where you were not liked for just your money or looks or power or bending abilities. You were liked for your qualities, your personality. Your bravery or kindness or determination.
It was much easier to be happy when Zuko didn't need to worry about being perfect.