One possible reason could be that he has received some kind of ancient power or curse. Maybe he stumbled upon a hidden jutsu during one of his adventures that gives him this ability. Another reason could be that it's a result of some experiment gone wrong. For instance, Orochimaru or some other mad scientist - type character in the fanfic might have been experimenting on Naruto and accidentally gave him this power.
Perhaps it's a gift from a god - like entity. In the Naruto universe, there are many powerful beings. It could be that one of these beings, seeing Naruto's potential for change or his good heart, bestows upon him the ability to remove bloodline. It might also be a form of karmic retribution. If some bloodline abilities have been misused in the fanfic's world, Naruto is given this power to correct the imbalance. Also, it could be related to his own Uzumaki bloodline having some hidden aspect that, when combined with certain events, gives him this unique ability.
Poison or some sort of harmful jutsu effect. Maybe an enemy uses a special poison or a jutsu that slowly weakens Naruto's body. In the fanfic, this could be a new and unique type of attack that he has not encountered before, and his body is not able to withstand it, resulting in fainting.
A possible plot might involve Naruto being exposed to some ancient and powerful knowledge or artifact. This discovery gives him the means to 'destroy' bloodlines in the sense that he can change the very nature of chakra within a person. He might use this new - found ability to break the cycle of bloodline - based power hierarchies. He could start with the major clans like the Uchiha and Hyuga, and as he spreads his influence, the concept of bloodline superiority slowly crumbles, leading to a new era in the Naruto world where a person's worth is determined by their own efforts and skills rather than their bloodline.
One possible reason could be that he is influenced by Orochimaru's techniques. Maybe he discovers some of Orochimaru's old research and figures out how to use snake summoning for his own good. Another reason might be that he is trying to find a new power source to defeat a very powerful enemy that normal jutsu can't handle.
Perhaps in the fanfic, Hinata has fallen in love with someone else. It could be a new character introduced in the fanfic's universe or someone she has come to know better over time, leading her to reject Naruto.
In some fanfics, there could be a misunderstanding. Suppose Kushina did something that Naruto misinterpreted as harmful to him or his friends. This misinterpretation could lead to his hatred. For example, if Kushina was involved in a mission that Naruto thought put the village at risk, but in reality, she had no choice.
One reason could be a major betrayal. For example, if his friends turned on him, it might shatter his idealistic view and push him towards violence. In fanfic, an author might explore this by having a false accusation against Naruto within the village, causing him to lose faith in the people he once trusted.
One reason could be that the fanfic writer wants to deviate from the original narrative where Naruto gradually gains acceptance. They might want to put him in a situation where he has to struggle more with being unwanted to make the story more interesting. For instance, they could write a scenario where new characters are introduced and they shun Naruto for some reason.
One possible reason could be a misunderstanding. Maybe Naruto misinterprets Hinata's actions or words and distances himself from her. For example, if Hinata is trying to be helpful in a certain situation but Naruto takes it the wrong way. Another reason might be external influence. If there are other characters who try to drive a wedge between them, like some jealous rivals who spread false rumors about Hinata to Naruto. Also, Naruto's own insecurities could play a part. He might feel that he's not good enough for Hinata and decides to let her go on his own accord.
It could also be that Naruto is forced to leave Sakura due to some external threat or danger. For instance, if there is an enemy targeting Naruto and he fears that being around Sakura will put her in harm's way, he would choose to leave to keep her safe. This is in line with Naruto's selfless nature as seen throughout the series.
One possible reason could be that Naruto has faced too many betrayals. Maybe his friends turned on him in the fanfic, which made him lose faith and stop caring.