One possible motivation could be power. Orochimaru is always seeking more power, and Naruto has the power of the Nine - Tails. He might think that by killing Naruto and somehow harnessing the Nine - Tails' power, he could become even stronger.
Maybe Orochimaru wants to disrupt the balance in the ninja world. Naruto is a major force for good and stability. By killing him, Orochimaru could create chaos, which he might enjoy or think he can benefit from. Also, Orochimaru has a history of experimenting on powerful beings, and Naruto with his unique abilities would be an interesting subject for him, so he might kill Naruto just to study his body.
One possible motivation could be mind control. Maybe an enemy uses some powerful jutsu to take over Naruto's mind and make him do it against his will. However, this would be a very dark and extreme take on the Naruto universe.
In some fanfics, Naruto might use his new and powerful jutsu that he has mastered over time. Maybe he combines his Sage Mode with the power of the Nine - Tails in a unique way that Orochimaru can't counter. For example, he could use the Nine - Tails' chakra to enhance the range and power of his Sage Mode attacks, and then catch Orochimaru off - guard.
It depends on the specific fanfic. Some authors might come up with this plot twist to explore different character motivations and conflicts. In others, it might not be the case at all.
One possible plot could be that Naruto, as Orochimaru's son, struggles with his identity. He might have Orochimaru's scientific genius but also Naruto's determination. He could be shunned by the village at first due to Orochimaru's bad reputation. But then, he uses his unique skills to prove himself, perhaps by developing new jutsu that combines Orochimaru's snake - related techniques with Naruto's own chakra - based powers.
One possible plot could be that Naruto, feeling ostracized in Konoha due to his jinchuriki status, decides to join Orochimaru. Orochimaru, seeing Naruto's potential, trains him in some dark and forbidden jutsus. Naruto might start to change, becoming more cynical. He could use his newfound powers against those in Konoha who once shunned him, leading to a series of battles between him and his former friends like Sasuke and Sakura.
Perhaps Naruto goes to Orochimaru in an attempt to redeem him. Naruto has a strong belief in the good in people, and he might think that he can convince Orochimaru to stop his evil ways. He could offer Orochimaru a chance at redemption, like a new start in the Hidden Leaf Village if he gives up his dark experiments and ambitions. This would lead to a complex relationship development between them, with Orochimaru being skeptical at first but gradually considering Naruto's offer.
An Orochimaru Wants Naruto fanfic might revolve around Orochimaru's attempts to capture Naruto for his unique chakra. He might believe that Naruto's chakra can help him in his research on immortality or in creating more powerful jutsus. It could also be about how Naruto resists Orochimaru's advances and the battles that ensue between them. Another aspect could be Orochimaru trying to manipulate Naruto's friends to get to him.
He could have been exposed to some dark secrets about the ninja world that made him lose faith in the traditional ways. Madara had his own reasons for his actions, and if Naruto discovers similar things, he might start acting like him. For example, if he finds out that the villages have been using ninjas in unfair or unethical ways for a long time, he could turn to more extreme measures like Madara did.
Maybe the writer just wants to be different. Since Naruto is usually seen as a hero, they might think it's edgy to write him as a loser.
Naruto might learn some very dark and powerful jutsus. Orochimaru is known for his forbidden jutsu knowledge. So Naruto could become a much more dangerous fighter but also risk being influenced by Orochimaru's immoral ways.