I've said it in a different thread. Most likely, Aang hasn't admitted his feelings until now because he feels unworthy of love for failing his duties as the Avatar twice now. Katara probably feels unworthy for being a peasant in love with the Avatar. It's been obvious Aang has had a crush on Katara since episode 1. Likely, she didn't start thinking about it until "The Fortuneteller."

I just don't get the feeling that Katara would have kissed him back if she didn't have feelings like that. If she did just think of his as a friend or brother, we would have seen her look guilty at some point after that for leading him on. I think we can all agree that no matter what kind of love she has for him, she would be guilty for hurting him in any way. And she knows that will hurt him more than anything else she could ever do.

As for why they never admitted their feelings before, that's how teenagers in love are. We're talking about two people that have very little romantic experience. The only guy Katara's age was Sokka until they left home. Aang lived in a monastery with a lot of other boys. Though it isn't conclusive proof, Aang has never talked about having had female friends. Both have feared that the other doesn't feel for them like they do, but they also fear they keep losing chances for something more. Aang probably came up with the idea because of his hallucination. Both seemed to have had the same intention in that scene: admit how they feel because tomorrow might be too late. The situation reached a point where there was something far worse than being rejected. And for two inexperienced teens, rejection can be one of the scariest things imagined.