First off, sure his motivation for hunting down the Avatar isn't necessarily bad. But that doesn't excuse the things he did in order to catch Aang. In the first episode he attacks a Water Tribe village and threatens to burn it down if Aang doesn't go with him. He also burns down the Kyoshi village trying to get to Aang. And there are many more destructive things he does in his quest to regain his honor. He has no respect for anyone or anything but his own quest. The other thing is that he doesn't care what will happen to Aang after he hands him over to his father. And he has little care for the war that's being fought all around him throughout the world.

Zuko is not exactly a nice person at the beginning of the series. He's selfish, obsessed, ruthless and consumed with rage. He's not wholly bad, he does care about his uncle and he isn't totally inured to the pain of others but most of the time he has blinkers on, so obsessed with his own path that he doesn't even notice the damage he leaves in his wake. He has to learn a lot and go through many travails, make a lot of mistakes before he becomes a good person. Which is what makes him a truly awesome character. The best characters have both light and dark inside of them, make mistakes- life changing mistakes- and learn from them.

And on a sidenote I think comparing Zuko's banishment from his home- it's illegal for him to set foot on Fire Nation soil- and brutal burning of his face and subsequent scarring to having his cellphone taken away is just weird. Banishment is not like being grounded. Having your father burn your face while you knelt before him is not like having your cellphone taken away. These things took away Zuko's childhood, damaged him mentally, emotionally and physically. It makes him a sympathetic character but it doesn't make his actions noble.

Zuko isn't a bad guy, he's just confused and angry and wondering why his life is so hard.he sees one hope and clings on to it desperately. He is obsessed with himself, but yet he cares about his uncle. His quest is hard.

zuko is not a bad gay.hes just confused.but in fact the life wasnt
right with him.how can he be a good gay ,when his dad and sister hate him.they have always lie him and always have run to him the wrong way..?poor him!!!like irise withthesun said,his life was so hard,but yea,his uncle was like a brother for him.his lucky for this.
and now that im here,i most tell you somethin,in avatar,the legent of korra,zuko will die.im very,very,very ...sad about this.good bye zuko!!!