Katara is what drives him. Without Katara, Aang has nothing to fight for, nothing to live for. Why shouldn't he and Katara be together? Because he's the Avatar? Because he has to put the world before her? Aang is a 12-year old boy who has risked his LIFE to bring peace over and over again, and has asked for nothing in return. After all he has done, the love of a beautiful, compassionate girl is very little to ask for.
I think you people are saying that Aang is better off without Katara because you want her to end up with Zuko. If that's the case, then this is just another way of preaching your ship. Stop trying to convince everyone that ZuTara is better, because we're all tired of hearing your nonsense.
One more thing: If you would break Aangs heart just so that Katara can end up with Zuko, then that is very sick and cruel.