Another reason might be revenge. There could be a character who has a grudge against Inuyasha or someone close to him. So, they kidnap him to make him suffer or to use him as bait to draw out his friends. For example, if there was a demon whose family was slain by Inuyasha in the past, they might kidnap him for revenge.
It could also be a case of mistaken identity. Some other powerful force might be after a different half - demon with similar powers as Inuyasha. And in the chaos of the situation, they end up kidnapping Inuyasha instead. This could lead to all sorts of comical or dangerous situations as Inuyasha tries to convince them of their mistake.
The Naraku would be a likely kidnapper. He is always plotting against Inuyasha and trying to get his hands on the Tessaiga. Kidnapping Inuyasha would be a way for him to either steal the sword or find a way to break Inuyasha's spirit so that he can no longer oppose him.
Another motive could be related to her family. Maybe there was some sort of blood feud or an old grudge against the Grangers. The kidnappers could have thought that by taking Hermione, they could get revenge on her family. In some fanfictions, there are secret magical families that have long - standing rivalries, and Hermione's kidnapping could be part of that.
Well, it might be that the kidnapper has some sort of medical need that they think Kaoru can fulfill. Since she's a nurse, they could be desperate for medical attention that they can't get through legal means. Or perhaps there's a villain in the fanfiction who just wants to create chaos in the hospital by taking one of its nurses, and Kaoru happened to be the unlucky one.
One possible motive could be ransom. Maybe someone wants a large sum of money from Philip's family or friends. Another could be revenge. Perhaps Philip has unknowingly wronged someone in the fanfiction world, and this is their way of getting back at him.
One possible motive could be to use Miko as a bargaining chip. Maybe the kidnappers want to exchange her for some valuable object or information within the Transformers' world. For example, they might be after a powerful Energon source or a secret Autobot technology.
A common plotline is that a main character like Kagome is kidnapped by a powerful demon and Inuyasha is the only one who can save her. He has to use his strength and the power of his sword. Another is when Inuyasha accidentally kidnaps someone due to a spell or misinformation.
Maybe Dumbledore believes that Harry has some hidden power that is being corrupted by the environment at Hogwarts. So, he kidnaps Harry to a secluded place to train him and help him control this power without any distractions or negative influences from other students or even some of the teachers.
Perhaps it's about love in a twisted way. Sebastian might be obsessed with Clary and think that by kidnapping her, he can make her his. In some fanfictions, characters with a warped sense of love do extreme things like this. He could also be trying to use Clary as a pawn in a larger scheme against the Shadowhunters. By having her in his control, he can manipulate the situation to his advantage.
One possible motive could be misinformation. Maybe Bucky was misled to believe the OC was a threat to someone he cares about. So, he kidnapped the OC to prevent them from causing harm.
Shego might kidnap Kim Possible in fanfiction because of jealousy. Maybe Kim always gets the credit and Shego wants to show that she's just as capable. So, she kidnaps Kim to prove a point.