AN: THE GREAT 2014 EDIT.
Disclaimer: You can bet certain things would never have become canon, were I the owner of Naruto.
Naruto never understood why anyone would want to live forever, but then it took him a long time to understand how to live in the first place.
Survival, now. Survival he knew. Deep in his bones, the oldest animal instincts, he knew how to run and fight and hide and steal – and sure, stealing was wrong, but his stomach felt hollow and empty and that shopkeeper didn't have to live off an orphan's allowance, and okay, so he got beaten up a lot, but the bruises never lasted long, and the point was that he was alive. Survival was the only religion anyone knew in his district.
(Surviving affected him more than he or anyone else ever realised. Forget healthy eating, you need to eat enough to live, and if the easiest food you can get your hands on is ramen then say hello to your new staple food. Forget winning a fight, your priority has to be getting away by any means necessary, so if you never win a fight at school but can outrun chuunin and know the sewers like the back of your hand, well – so be it.)
On the heels of survival came isolation and all that it meant. There was no-one waiting in Naruto's apartment when he got home. In all his short years there had never been a morning when he got out of bed looking forward to seeing someone. You survived until you didn't and that was it, that was the sum total of your existence: this was Life as far as Naruto was concerned.
He did have one thing on his side, in his skillset: defiance. Pranks and bright clothes and loud voice – he could defy anyone and anything, hell, just his staying alive was an act of defiance. (One day he would tell someone this. One day he would tell someone that he yelled his words and wore kill-me-orange because it was a way of saying, fuck you, you bastards, I'm alive.)
Defiance became so much of him. He took the words they gave him – powerless, foolish, troublemaker, shunned – and flipped them to read powerful, wise, good, trusted, and there it was staring him in the face, the title of Hokage. And suddenly Hokage was his life's goal. The ultimate act of defiance: what better goal was there for him?
Survival and defiance are usually mutually exclusive, but Naruto never believed in impossible things. Survival without cynicism, and defiance without bitterness: Naruto balanced them, imperfectly, gloriously, and they melded into something that had no name but his. (And when he grew older he would achieve more mutually exclusive things, like staying loyal to Konoha and not killing Sasuke, because he understood how to balance on the edge of a knife, knowing instinctively that to fall either way would spell destruction.)
Life began with Iruka-sensei, with someone who was father and brother and teacher all at once, whose presence felt warm around him like an embrace, whose scolding he didn't mind because it meant someone cared enough to want him to be better. (Life began with a shuriken ripping through that strong back –) Life was intense, euphoric, Naruto wanted more of it, more more more, never enough and always enough, like that old saying, enough is as good as a feast.
He graduated; he met Sasuke and Sakura-chan and Kakashi-sensei, and life grew faster and brighter and more intense, colour spreading across it like fire across paper. He still had plenty of use for defiance around them, but Naruto had never in his life expected to be offered respect. (Only wanted it, desperately.)
On the mission to Wave it really hit him for the first time that there were people who wanted to take life away. They tried to take life away from Sasuke – they tried to take Sasuke away, tried to send Naruto's life back into greyscale again –
Naruto's rage was fire and sharp teeth and eyes in the night.
(And now he had a reason to become Hokage, a reason to seek power and wisdom and goodness and trust. Now he understood the abyss between surviving and living, and felt a compulsion to keep anyone else from falling into it.)
And even then, Naruto still didn't understand why someone would want to live forever. Because that desire, as far as he could tell, was the desperate urge to survive no matter what, and surviving was the furthest thing from living he knew.
(Because the only people he ever saw who wanted to live forever were those who were prepared to take life from others, and that was too high a price to pay.)