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.
It could be an old hermit who has been living in seclusion for years. This hermit has mastered the Goken and sees potential in Naruto. So, he decides to teach Naruto this powerful technique.
One aspect of Naruto and Kakashi family fanfiction could be the idea of Kakashi mentoring Naruto not just as a sensei but as a family member. This could involve Kakashi helping Naruto understand the importance of family values, which Naruto lacks growing up. In fanfiction, we could see Kakashi inviting Naruto to family - like gatherings with Team 7, making Naruto feel more included and part of a family unit.
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.
Well, it could strain their relationship. Avoidance usually creates distance, and in this case, Kakashi might feel hurt or confused as to why Naruto is avoiding 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.
Their relationship is like a mentor - mentee bond. Kakashi has trained Naruto, and when he sees Naruto achieve great things, it can be overwhelming. For example, when Naruto masters a new jutsu that Kakashi thought was difficult for him, Kakashi might cry out of joy for Naruto's accomplishment.
It could become strained. Naruto snapping at Kakashi would create an initial rift between them. Kakashi might be taken aback by Naruto's outburst and Naruto, after snapping, might feel a bit guilty but also stubborn about his feelings, which would make the relationship tense for a while.
Naruto might be the better singer in terms of energy and enthusiasm. His loud and boisterous nature could translate into a powerful and engaging singing voice. He'd probably belt out songs with great passion, getting the audience pumped up.
Sasuke could be a great addition. He could be a rival to Naruto even at a young age, and Kakashi would have to deal with their constant bickering. His brooding nature would add an interesting dynamic to the story.