One possible motive could be a misunderstanding. Maybe Hiashi mistakes Naruto for an enemy who has infiltrated the village in disguise. Another reason could be related to clan politics. If Naruto somehow gets involved in a situation that threatens Hiashi's clan interests, Hiashi might take extreme measures.
Perhaps Naruto accidentally discovers a dark secret of Hiashi's family. To keep the secret hidden, Hiashi decides to kill Naruto. For example, if Naruto finds out about some illegal or immoral actions that the Hyuga clan has been involved in, Hiashi may see him as a threat to the clan's reputation and existence.
One possible reason could be that Naruto is in love with a Hyuga clan member. Since Hiashi is the head of the Hyuga clan, Naruto might think it's proper to ask for his blessing. For example, if he has feelings for Hinata, Hiashi's daughter. Hiashi's approval would mean a lot in terms of family and clan acceptance.
Well, it could be about Naruto growing up in the Hyuga clan. Maybe he discovers his true parentage early on and has to deal with the expectations and politics of the clan. He might learn the Gentle Fist technique in a different way than Neji or Hinata.
Perhaps in this fanfiction, Naruto meets Hiashi during a time of crisis in the Hidden Leaf Village. Hiashi, being an elder and a respected figure, is involved in the village's defense plans. Naruto, eager to help, wants to be part of the action. Hiashi initially doubts Naruto's abilities but is soon proven wrong. They then work side by side, with Naruto's Uzumaki chakra and Hiashi's Hyuga skills combining to create a powerful defense against the enemy.
Maybe Hiashi adopts Naruto because he realizes that Naruto is a key to uniting the village. As Naruto becomes part of the Hyuga family, he starts to influence the clan's view on outsiders. He might introduce some new training methods that he learned from Jiraiya. Naruto could also have a role in protecting the Hyuga's secrets, like the Byakugan. He would grow in a different environment, and this would change his relationships with characters like Sasuke and Sakura in new and unexpected ways.
Perhaps in this fanfiction, Jiraiya discovers that Naruto is going to be the cause of a major catastrophe in the future. He might have seen a prophecy or some sort of sign that convinces him Naruto has to die to prevent this. It could also be that Jiraiya has been misled by false information about Naruto, which makes him think that Naruto has become an evil force that needs to be eliminated.
It could be that Yagura had some secret plans that would endanger the balance among the ninja villages. Naruto, having a strong sense of protecting peace, discovers these plans and decides that eliminating Yagura is necessary. For example, if Yagura was planning to use a powerful and dangerous jutsu that could destroy multiple villages, Naruto would act to prevent it even if it means killing him.
In the 'boruto kills naruto fanfiction', a motive could be a power struggle. Boruto might believe that Naruto's power is holding back the village's growth or his own potential. He could think that by eliminating Naruto, he can bring about a new era of power in the Hidden Leaf. Also, it could be out of desperation. If Boruto is in a situation where he believes that killing Naruto is the only way to save someone he loves, like his mother or a friend, he might take such a drastic step.
One possible motive could be that Kakuza has committed some heinous crimes against the Hidden Leaf Village. Maybe he has been involved in secret attacks on the village or has been plotting something really bad that would endanger the lives of many villagers. Naruto, being the protector of the village, would then take it upon himself to stop Kakuza by any means necessary, which unfortunately might end up in killing him.
Naruto might convince Hiashi by pledging his loyalty to the Hyuga clan. He could say that he'll uphold the clan's values and traditions. Also, Naruto could mention how Hinata has been a positive influence on him, which shows his respect for her. He might also talk about his plans for the future and how Hinata will be an important part of it in a way that benefits both the Uzumaki and Hyuga clans.
In the long run, the absence of Naruto would mean the loss of his positive influence. He was a symbol of hope and unity. Without him, the ninja world might fall into more despair and division. The new generation that looked up to Naruto would be left without their role model, and the future of the ninja world would be much darker.