Maybe Sasuke teaches him the Chidori in a moment of camaraderie. And for the Rasengan, it could be an older and wiser Naruto from the future who travels back in time to teach his younger self.
It could be Kakashi. Since he's already Naruto's teacher and he knows both techniques. He could guide Naruto in understanding the intricacies of the Chidori, like how to form the lightning - chakra in his hand, and for the Rasengan, he could give more advanced tips on chakra control.
In a fanfiction like this, the plot might involve Naruto struggling to master both techniques. He could start by observing Sasuke use the Chidori and then try to incorporate its lightning - based power into his own jutsu. For the Rasengan, he might have new insights while training, perhaps finding a way to combine it with the Chidori for an even more powerful attack. Along the way, he would face challenges like controlling the chakra flow for both techniques and dealing with opponents who are also after these powerful jutsus.
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.