Maybe there was some sort of divine interference or prophecy. For instance, a prophecy foretold that a child of Artemis would be the key to saving the world from a great threat. So, the gods found a way to make it happen, despite Artemis' vow of chastity. It could also be that some dark magic forced Artemis into a situation where she had to bear a child, and that child was Percy.
One possibility is that Artemis made a deal with another powerful entity. She might have traded something very precious in order to have a child, Percy, who she believed could bring about a new era of peace or balance in the world of gods and demigods. Another idea is that there was a misinterpretation of a powerful spell or ritual. Artemis was involved in some ancient magic, and it accidentally resulted in her becoming Percy's mother.
Perhaps Percy has lost someone very dear to him in a battle. He might feel guilty for not being able to protect that person, which has led him to this dark state of mind.
She might start to compare the real Percy (if he exists in the same universe) to the fan - created versions. This could lead to misunderstandings or unrealistic expectations.
One possible reason could be differences in their divine natures. Percy is a son of Poseidon, a god associated with the sea and a more fluid, emotional element. Artemis is a virgin goddess of the hunt, very strict and unyielding in her ways. This contrast in their essences might lead to clashes and Percy's dislike.
In the fanfiction, a possible backstory could be that Naruto, after achieving great power and peace in his own time, decided to use his abilities to explore the past. During this exploration, he accidentally or purposefully got involved in the lives of his ancestors. He might have fallen in love with a woman from the Uzumaki clan in the past and had children. These children then passed on their genes through generations until Kushina was born. It could also be that there was some sort of experiment by an ancient shinobi that went wrong or right (depending on how you look at it). This experiment somehow connected Naruto's future self to be Kushina's grandfather by altering the fabric of time and family relations in a very strange way.
Well, perhaps in this fanfiction, Artemis betrays Percy for Orion due to a prophecy. There could be a prophecy that states that Orion and Artemis together will bring about some great change or prevent a huge disaster, and Artemis believes she has to choose Orion over Percy to fulfill it. Also, Orion might have some sort of leverage over Artemis that forces her to turn her back on Percy.
One possible reason could be a misunderstanding. Maybe there was some miscommunication or false information spread that made Artemis think Percy had done something unforgivable. For example, if Percy was wrongly accused of harming one of Artemis' beloved creatures or desecrating her sacred places.
One reason could be the contrast between their characters. Percy is often seen as a heroic, adventurous type, while Artemis is a goddess of the hunt, more reserved. The idea of them as secret lovers creates an exciting 'opposites attract' scenario.
It would be a complex dynamic. Artemis is known for her aloofness and strictness. Percy, on the other hand, is a bit of a rebel. So, initially, there would be friction. However, as Percy starts to learn from Artemis, like her hunting techniques and her connection to the moon, he would start to conform more. Artemis would in turn start to see Percy as more than just a wayward demigod and would protect him fiercely. They would form a bond that is both teacher - student and mother - son like.
One common theme is the exploration of Percy's new powers or abilities. Since Artemis has her own set of powers, Percy might gain some of those, like enhanced archery skills or a closer bond with nature. Another theme could be the change in Percy's relationships. His relationship with his friends and other gods would be different because of his new mom.
Well, it could be for the sake of creating a unique and complex backstory. Maybe the author wanted to explore a relationship that didn't work out due to their different natures. Artemis is a goddess with her own set of values and Percy has his own hero - like qualities. Their clash of personalities could be a reason for the divorce in the fanfiction.