If Naruto was in Kakashi's generation in fanfiction, he would probably change a lot of things. He has that determination and willpower. Maybe he could have prevented some of the tragedies that happened in Kakashi's time, like the fall of Obito. His presence might also make Kakashi less of a lone wolf as Naruto has a way of bringing people together. And he would surely learn some new jutsu from the older shinobi in that generation.
Well, in such a fanfiction, Naruto would be a contemporary of Kakashi. He might have different relationships with the characters of Kakashi's generation. For example, he could be closer friends with Obito and Rin. His skills might also develop in different ways as he would be exposed to different training methods and challenges that were relevant to that generation. He could have a different perspective on the Uchiha clan's issues as he would be more directly involved in that era.
Well, Naruto might be more reserved in Kakashi's generation. He would be among older and more experienced ninjas. He would have to prove himself more quickly. He might not have as much room for his wild and carefree antics as he did in his own generation. He'd be learning from different mentors too, which could shape his jutsu usage and battle strategies in a new way.
He could have a huge impact. For example, in the fight against the Akatsuki, Naruto's unique abilities like the Nine - Tails' chakra could change the tide. His positive attitude might also inspire the more jaded ninjas of Kakashi's generation to be more hopeful.
The story would change a great deal. Naruto's presence in Kakashi's generation could mean an earlier end to the Third Great Ninja War. His ability to inspire and his combat skills could turn the tides of battles. For instance, if he was there during the Kannabi Bridge mission, things might have gone very differently. He could have kept Obito from getting crushed and perhaps changed the fates of many.
It could be due to a misunderstanding. Kakashi might think that Naruto is getting involved with something dangerous or has some potential that he can't handle. So, in his warped way of thinking, he abandons Naruto to protect him from himself or from some unknown danger.
Maybe Kakashi is preoccupied with other important missions. He is a highly - skilled and often - needed ninja. There could be some top - secret missions that require his full attention, leaving him no time to train Naruto properly.
Another reason could be related to Kakashi's past actions. If there are some secrets or things Kakashi did in the past that come to light and Naruto doesn't like them, he could snap at Kakashi. Naruto has a strong sense of justice and loyalty, so if he feels betrayed or misled by Kakashi, his reaction could be to snap.
One reason could be that he saw Naruto's potential later on and realized he could have been much stronger if he had trained him earlier. For example, Naruto has a great deal of chakra and tenacity, and with proper training from Kakashi earlier, he might have reached new heights faster.
One possible reason could be that Kakashi believes Naruto's sword holds some special power or secret that is crucial for a mission or for the safety of the village. Maybe he has discovered some threat that only the sword can counter, and he needs it in Naruto's possession.
If Kakashi adopted Naruto, it might change Naruto's path of development. He could receive earlier and more specialized training, and also have a stronger sense of family. This could have a significant impact on his personality and goals.
There might be. Fanfiction writers often like to play with the established relationships in the Naruto universe. Since Naruto has a complex world with many interesting characters, it's not unusual for someone to write a story where Naruto becomes Kakashi's sensei in an alternate timeline or some other creative scenario. It could be an interesting take on the characters' development and the overall story.