... the way he did in the final episode. (Note: Wow, two topics in one day from someone who's a major lurker. Sorry if there's a topic for this, but I didn't see any)
Anyways, I admit I wasn't sure of the logic of this either... until I read someone's explanation on deviantART. This next part isn't mine, it belongs to Kawa-Misuterii and deviantART and I'm only using this to give an explanation to confused fans like I was:
"One last thing.............don't kill me, but I do believe Aang let Katara go. There's a spiritual difference between caring about something or someone, and being attached to something or someone, and Aang wouldn't have been able to go into the Avatar State in Ba Sing Se if he didn't let her go. The fact that his chakra was locked was because Azula physically screwed something up with his body with the lightning bolt(remember the chakras are all based in different areas of the body) So it only makes sense that he manages to right himself physically, thus inducing his chakras to align themselves."