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.
Naruto might approach Yagura with honesty. He would probably start by telling Yagura that he knows he's in a bad situation with the Akatsuki. Naruto could share his own story of being ostracized in Konoha at first and how he overcame it. This would make Yagura see that Naruto can understand his pain and might be more receptive to Naruto's help.
The plot could involve Yagura being freed from the control of the evil forces that once manipulated him. Naruto, being the hero he is, senses something strange about Yagura. He then uses his shadow clones to investigate. When he discovers the truth, he uses his chakra to break the hold on Yagura. After that, they form an alliance to help the Hidden Mist Village recover from the damages caused by Yagura's previous actions under control.
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 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.
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.
Maybe Orochimaru could be the antagonist. He hears about Naruto's encounter with Yagura and wants to use their connection for his own evil experiments. He might try to capture Yagura again (if he was once under Orochimaru's control) or manipulate Naruto into doing something that would harm Yagura and the relationship between the two villages.
In the original storyline, Yagura was the Fourth Mizukage who was being controlled by Obito. He was more of a victim. But in this fanfiction, Naruto kills him, which is a huge deviation as Naruto is usually about saving people. In the original, Naruto tries to understand and redeem his enemies, not kill them outright.
Well, Naruto is known for his determination. He would probably first try to understand Yagura's situation. Maybe he discovers that Yagura was being manipulated by the Akatsuki through some sort of jutsu. Naruto could then use his own chakra to counter that jutsu and free Yagura's mind. After that, Yagura might be so grateful that he helps Naruto in his fight against the Akatsuki.
It could also be related to a prophecy or a pre - determined fate in the fanfic's plot. There might be some kind of dark prophecy that says Kawaki has to kill Naruto to prevent a greater evil. Or perhaps Kawaki is being controlled by an external force that has a vendetta against Naruto and uses Kawaki as a tool to carry out the murder.
In fanfiction, the 'Naruto x Yagura neglect' could imply a relationship where Naruto is somehow involved with Yagura, but there is neglect present. This might be explored in terms of their character interactions. For example, if Naruto fails to understand Yagura's past traumas which leads to a form of neglect in their relationship. It could also be a situation where the storyteller is trying to show the consequences of such neglect on both characters' development and how they deal with the emotional fallout.