What I get out of this is that Naruto is trying to tell Sasuke “I’m not doing this because I feel like I have to fix you or our broken team, I’m not doing this because I made a promise to anyone. I’m doing this because we were both alone, and now I’m not but you still are. You know I could never let you hurt Konoha, but that’s not the point. Even if I don’t save you, even if I can’t convince you, even if I have to kill you to stop you, I’m going with you, because I will never let you be alone again.”
Naruto, more than anyone else, knows that’s why Sasuke was so hurt, why he’s still hurting, and he’s never going to let his best friend die alone.