Here's a very interesting kataang reference from the Earth Kingdom Chronicles, we probably didn't notice!
Back in the show from 'The Guru' episode, Aang said :
"Why would I let go of Katara, I love her"
Thankfully with the Earth Kingdom Chronicles, we get to explore more of Katara's inner thoughts and from 'The Desert' episode :
"After everything he's done, everything he's meant to me, I am not letting go"
Katara, eventually cannot let go of Aang as well but it was pretty obvious in the show that they both cannot detach themselves from each other, they've a very deep connection, but this awesome detail add a lot to their relationship.
Aang in the first place, is not letting go as an act of selfishness as he appreciates his friendship with Katara, he values this connection they have together. Plus, by learning that Katara is the reincarnation of the love of his people, this added something more meaningful to him over cosmic energy.
And for Katara, she is not letting go as an act of selflessness since unlike the others, she's overcoming her fears of the Avatar State to comfort her friend, she's showing to Aang that his feelings are valid after losing his best friend, this is more important to her over protecting herself.
This is another description of how they balance each other in many ways, one for being selfish of not letting go and one for being selfless! This is soulmatism.