One possible motive could be that in the fanfiction's plot, Illya might be influenced by some dark magic or external force that compels her to kidnap Shirou. For example, if there is an evil entity controlling her actions, it could use her as a tool to get to Shirou for some unknown, perhaps sinister purpose related to his powers or his connection to other characters in the story.
Another motive could be related to some sort of power play. Eric might want to use Sookie as a bargaining chip. Since Sookie has her special abilities, other powerful entities in the fanfiction world might be interested in her. Eric could kidnap her to gain an advantage over his rivals.
It could also be for power. In the fanfiction world, Sebastian might think that by kidnapping Kurt, he can gain some sort of power over the New Directions or the McKinley High glee club. He might want to use Kurt as a bargaining chip to get what he wants from them.
One possible motive could be a misunderstanding. Maybe Steve believes Tony has done something that endangers the team or the world, but he's misinformed. Another could be that Steve has been mind - controlled. In some fanfictions, external forces take over Steve's mind and make him do things he wouldn't normally do, like kidnapping Tony.
One possible motive could be protection. Annabeth might think that there is a threat to Percy that she can only handle by taking him away from the situation. For example, if there's a prophecy that puts Percy in danger and she believes she can keep him safe in a hidden location.
Maybe he wants to use Ichigo as a bargaining chip. If there are other forces or characters in the fanfiction world that Kisshu is in conflict with, he could kidnap Ichigo to gain an advantage over them. For example, if there are rival groups vying for power or resources, Ichigo might be valuable to them in some way, and Kisshu could use her to negotiate. Another motive could be that he believes Ichigo has some sort of special power or knowledge that he wants to extract from her, and kidnapping is his way of getting close enough to do so.
Overall, their relationship in fanfiction is often explored in different ways. It can range from a brother - sister - like bond to a more romantic relationship. The fanfic authors play with their personalities and backstories to create unique and engaging stories. For instance, some fics might explore how their different upbringings affect their relationship, with Shirou's more normal upbringing contrasting with Illya's complex magical heritage.
Maybe in the fanfiction, Naruto is being controlled by some dark magic or a powerful enemy. This could force him to kidnap Lemon against his will.
Maybe Sirius wants to train Harry himself. In fanfiction, he could believe that he has a better understanding of the Dark Arts and how to fight Voldemort compared to the professors at Hogwarts. So, he kidnaps Harry to start his own special training regime away from the school.
Popular shirou and illya fanfiction often focuses on their relationship. It might show their growing bond, like in 'The Growing Affection' where you can see how their feelings for each other develop over time. Another characteristic is exploring their different personalities. For example, Shirou's selfless nature and Illya's sometimes child - like yet strong - willed personality. Also, many good fanfictions put them in unique situations, like in 'Shirou and Illya in a Parallel World' where they face new challenges in a different world.
One possible motive could be ransom. If the mom is an influencer, the kidnappers might think she has a lot of money or valuable assets, and her family or sponsors would be willing to pay a large sum to get her back.