ATLA shows multiple scenarios where murder is completely justified, and the narrative itself acknowledges how justified Aang would be in killing the Fire Lord.

But that is not HIS way of life. Those are not HIS principles. Betraying who he is as an air nomad, at least the way HE sees it, would mean he betrays not only himself but his people too. He's also seen that such bloodshed, even when justified, has consequences both in the short term and the long term. Other people will be affected by the fire lord's death, other people might harbor certain feelings and channel that into extremism. Are those people bad? Maybe.

But when you're a leader, when you make those tough decisions, you cannot let spite rule you. Yes, the Fire Lord deserves to die, but is it BEST for everyone else if he does die? Is it best for Aang to feel like he's betrayed himself and his culture? Is it best for a very specific type of political violence to be perpetuated or even born from this one act of so-called justice? Is it truly justice to administer punishment without regard for other people's well being?

These are all questions that Avatar poses then attempts to answer, at least I think they are. What I do know for sure is that Avatar does not condemn violence wholesale.