The act of saving her could also make Naruto more protective of Koyuki in the future. He may see her as someone he has a special responsibility towards. And Koyuki may see Naruto as a hero figure, which would shape their relationship in a way that she always trusts him and values his opinions.
There might be a sense of indebtedness on Koyuki's part. She may constantly look up to Naruto and be willing to support him in whatever he does later in life. Their relationship could be one where Koyuki is always there for Naruto, because of what he did for her as a child.
One possible reason could be Naruto's natural sense of justice. He can't stand to see a child in danger, and Koyuki being a child at that time, Naruto's heroic nature kicks in. He has always been the type to help those in need.
On the other hand, Naruto's anger could also be a wake - up call for Boruto. If Boruto respects his father, seeing Naruto angry might make him realize his mistakes and try to change his ways, which could ultimately strengthen their relationship as they work through the issues.
It might also create a rift within their group. If their friends witness Naruto yelling at Sakura, it could cause tension among the whole group. Some might side with Naruto, thinking Sakura deserved it, while others might defend Sakura, leading to a divided group dynamic in the fanfiction.
It might create a rift between them. If Naruto feels that Sakura is always nagging and yelling, he could start to avoid her. In some fanfictions, this could lead to a period of estrangement where they don't work well together as a team. For example, Naruto might choose to go on solo missions instead.
It can initially create some tension. Naruto might act out in small ways, like being a bit short - tempered around Hinata. This could make Hinata confused and a bit hurt. But as the story progresses, it can also lead to more honest communication. Naruto realizes his jealousy is a sign of his deeper feelings for Hinata, and he finally confesses. This can strengthen their relationship as they start to understand each other better.
It could strain their relationship. Naruto's outburst might make Jiraiya realize that he has been misreading Naruto's needs, which could lead to a period of distance between them as they both reevaluate their connection.
It could strain their friendship. Naruto might start avoiding Sakura, which would make her realize she's done something wrong and try to fix it.
It can strain their relationship initially. Boruto might feel unjustly scolded and become resentful towards Naruto.
Jealousy can create misunderstandings. For example, if Naruto gets jealous, he might jump to conclusions about Hinata's actions and say something hurtful without meaning to. This could make Hinata feel sad and pull away from him, straining their relationship.
It could strengthen their relationship. Taking care of a child together requires cooperation and communication. They would have to work as a team to raise the child, which would deepen their bond. They might also discover new things about each other through the process of parenting.