Another reason could be that Naruto has made a promise to someone in the Hyuga clan. To fulfill this promise in the most honorable way, he decides to ask Hiashi for his blessing. It could also be that Naruto has a new idea or project that he believes would benefit the Hyuga clan, and he wants Hiashi's support, which starts with asking for his blessing.
Maybe Naruto wants to form an alliance or some kind of special bond with the Hyuga clan. By asking Hiashi for his blessing, he is showing respect and indicating his good intentions towards the clan. This could be related to some greater mission or plan in the Naruto universe that involves the cooperation of the Hyuga clan.
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.
Hiashi could be initially skeptical. Naruto has a reputation for being a bit of a troublemaker at times. But if Naruto presents a good case, Hiashi might warm up to the idea. For instance, if Naruto shows how his actions would bring honor and prosperity to the Hyuga clan.
Naruto asking for Hiashi's blessing in a fanfiction could lead to a whole range of scenarios. Firstly, Naruto might approach Hiashi with a lot of respect but also his usual bravado. Hiashi, being the head of the Hyuga clan, would have his own concerns. He might worry about how the other clans would react to a union between Naruto and a Hyuga. However, Naruto could counter this by talking about his dream of uniting the ninja world. His relationship with Hinata could be presented as a symbol of that unity. And as Naruto shows his understanding of the importance of family and clan, Hiashi could gradually come around and give his blessing.
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.
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 reason could be that Hiashi might see Naruto as a threat to the Hyuga clan's secrets or traditions. Naruto is often associated with unpredictable and powerful abilities, and Hiashi, being protective of his clan, may want to keep him at a distance to safeguard the clan's interests.
Maybe in the fanfic, there is a dark force that tries to manipulate Hiashi into attacking Naruto. The fanfic could explore how Naruto tries to reach out to Hiashi, to show him that they are being played. Along the way, they have an intense battle where Naruto shows off his new jutsus and Hiashi uses his clan's most secret techniques. In the end, they realize they were on the same side all along.
Maybe Hiashi is poisoned, and Naruto has to find an antidote. He could go on a journey to find a rare herb or seek the help of a medical ninja. Along the way, he might face various obstacles, but his will to save Hiashi would keep him going. He could also use his connection with the Nine - Tails' chakra to boost his search or fight against any threats.
In this fanfic, Naruto might save Hiashi in a battle situation. Maybe Hiashi is facing a powerful enemy that he can't handle alone, and Naruto steps in with his strong ninja skills. For example, if Hiashi is being attacked by a group of rogue ninjas, Naruto could use his Rasengan to fend them off.
Maybe Hiashi thinks Naruto fanfiction might contain inappropriate or untrue portrayals of the Naruto world and characters. He wants to protect Hinata from being influenced by such potentially inaccurate or improper content.
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.