One reason could be Naruto's power. In the Naruto universe, Naruto has great power, and both Itachi and Sasuke might see Naruto as a key to achieving certain goals. Itachi might want to protect Naruto because he sees Naruto as a force for good in the future of the ninja world. Sasuke, on the other hand, may view Naruto as a rival in terms of power and influence, and in fanfiction, this could lead to a fight between them over Naruto.
Itachi. He was a highly skilled and intelligent shinobi. His Sharingan abilities were extremely powerful, and he had a lot of combat experience. He also had a strategic mind, which would give him an edge in a fight over Naruto.
Their relationship could be developed through a series of flashbacks. For instance, Itachi could recall moments from Naruto's childhood that he observed while in the ANBU. These memories could make him see Naruto in a new light. Meanwhile, Naruto could learn about Itachi's past and the sacrifices he made. This exchange of knowledge could build a bond between them based on empathy and respect. In addition, they could train together in secret, with Itachi teaching Naruto some of his ANBU skills, which would also strengthen their relationship.
Naruto would adapt to Itachi's life in several ways. Socially, he'd have to get used to Itachi's connections and rivalries. For instance, his relationship with Kisame would be different as Naruto. He might try to influence Kisame in a more positive way. Emotionally, he'd have to deal with Itachi's internal struggles. Itachi had a lot of guilt and secrets, and Naruto would have to either come to terms with them or find a way to resolve them. And in terms of combat, he'd practice Itachi's signature moves over and over to make sure he could use them effectively in battle.
They could develop a mentor - mentee relationship. Itachi uses his knowledge of the Sharingan to teach Naruto new combat techniques. As they train together, they bond over their shared experiences of loss and their desire to protect the people they care about. Naruto might also help Itachi come to terms with his past actions and find some peace within himself.
One interesting aspect of Naruto Rule 63 Itachi fanfiction could be exploring Itachi's character from a different gender perspective. In these fanfictions, Itachi might have different relationships with other characters. For example, his bond with Sasuke could be portrayed in a new light, perhaps with more emotional nuances due to the gender - swap. Also, the way he approaches his mission and his loyalty to the village could be re - examined through this new lens.
At first, it's likely to be very awkward. Naruto is a very open and energetic person, while Itachi is more reserved. But as they are forced to spend time together because of the arranged marriage, they start to find common ground. For instance, they both care deeply about protecting the village in their own ways.
One reason could be for strategic purposes. Itachi was a highly strategic ninja. So, in fanfiction, Naruto might act like him to outwit a particularly difficult enemy. For instance, when facing an enemy who is a master of deception, Naruto could adopt Itachi's calm and calculating demeanor to see through the enemy's tricks.
Naruto might give Itachi some traditional Konoha food as a gift. Since Itachi has been away from the village for a long time, he might miss the taste of home.
Itachi would be very strict in Naruto's training, but also very caring. Naruto would look up to Itachi and try to learn as much as he can from him. As Naruto grows, he might start to have his own ideas which could sometimes clash with Itachi's. But through communication and understanding, their relationship would become deeper. Itachi would share his past experiences with Naruto, which would make Naruto understand the complexity of the ninja world better, and in return, Naruto's innocent and determined nature would slowly change Itachi, making him more hopeful about the future of the ninja world.