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.
Naruto could initially feel a great sense of loss and sadness. But as time goes on, he might start to look for new mentors or friends who can support him. For example, he could turn to Iruka-sensei more often or form closer bonds with his fellow classmates like Shikamaru or Choji. He'd rely on his inner strength and the relationships he already has to get through this tough time.
His ninja skills would probably develop in a different way. Without Kakashi's guidance, he'd have to figure things out on his own. This might lead to some unorthodox training methods and a unique fighting style. For example, he might focus more on his natural instincts and less on the traditional teachings he received from Kakashi. He could also form new alliances with characters who are also outsiders or misfits in the ninja world, creating a new support system for himself.
One possible reason could be that Kakashi is preoccupied with other important matters in the village. Maybe he has some top - secret missions or tasks assigned by the Hokage that demand his full attention, leaving him with little time to focus on Naruto.
One possible reason could be that Naruto might feel Kakashi is too strict with his training. Maybe Kakashi's methods are too harsh for Naruto, making him frustrated and gradually developing dislike.
One possible reason could be Kakashi's reputation as a strict and powerful teacher. Naruto might be in awe of his skills and fear making mistakes in front of him.
One possible reason could be that Naruto might be trying to prove his independence. He has grown and wants to show that he can handle things on his own without always relying on Kakashi's guidance.
One possible reason could be that Kakashi later realizes Naruto's potential. He might see how much Naruto has grown on his own despite being ditched, and feels guilty for not being there to guide him more. Another reason could be that Kakashi starts to understand the importance of Naruto in the overall story or the team's dynamic. Maybe he misses the bond they could have had if he hadn't ditched Naruto.
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.
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 in the fanfiction, Kakashi might have made a decision during a mission that Naruto strongly disagreed with. For example, Kakashi could have chosen to sacrifice something important to Naruto in order to achieve the overall mission objective.