He rejects her advice as well, and runs all the way to his vegetarian pacifist monk predecessor (surely he understands Aang's soul and will tell him what he wants to hear). He tells him the same thing that the others did. Aang's not a monk. He's the Avatar, the defender of the world, and he needs to grow up in a hurry and learn how to kill when it becomes absolutely necessary, because there are some people out there who simply cannot be reasoned with.
This is some serious shit. So how does the show resolve this impasse? Deus ex machina.
1. Yangchen is a woman. She was also a fucking beast. There's a reason no one thought to put a toe out of line when she died and Kuruk was such a poor Avatar.
2. No, none of them told Aang to kill Ozai. Aang was in the head space where he perceived all of heir advice as 'kill him'.
Roku's advice wax whatever he did, don't half ass it. Roku could have stopped the war if he'd killed Sozin. He would have ALSO stopped it if when Sozin told him the plan he actually talked with him. Instead he shouted him down and left.
Kyoshi tells him that only justice can bring peace. She left a corrupt king in charge on a promise to take care of his people in exchange for quelling a just rebellion and creating the Dai Li. She sought peace instead of justice.
Kuruk's tells him to actively shape his destiny. Kuruk was a lazeabout do nothing because of how peaceful things were after Yangchen. It cost him his wife who was taken by a spirit he should have already been doing something about.
And Yangchen told him that his spiritual needs didn't matter as he needed to protect the world.
Yangchen was a VERY successful Avatar.
My point being that none of them wanted Aang to specifically kill Ozai. Because he and we as the audience saw that as the only way, we heard what we expected to hear.
The Lion Turtle provided him with another option, but he still followed all of the previous Avatars' guidance.