One possible motive could be jealousy. Grindelwald might be jealous of Dumbledore's power and popularity in the wizarding world. By kidnapping him, he wants to prove that he is the more powerful one.
Grindelwald may see Dumbledore as a threat to his grand plans. Dumbledore has always been an advocate for peace and equality among wizards and non - wizards. Grindelwald, with his ideas of wizard supremacy, might think that by kidnapping Dumbledore, he can silence his opposition and continue with his plans of dominating the non - wizard world without Dumbledore getting in the way. Also, there could be some personal vendetta between them from their past encounters. Maybe Dumbledore once thwarted Grindelwald's plans, and this is his way of getting revenge.
In the fanfiction, Grindelwald could want to use Dumbledore's knowledge for his own gain. Dumbledore is known for his vast knowledge of magic, especially ancient and powerful magic. Grindelwald might believe that by kidnapping Dumbledore, he can force him to reveal secrets about magic that could help him in his quest for power. He may also think that having Dumbledore as a hostage would give him an advantage in negotiations with the wizarding community, making them more likely to submit to his demands.
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.
In a fanfiction, Dumbledore might steal out of desperation. Suppose there was a situation where a curse was about to be unleashed on Hogwarts, and the only way to stop it was by stealing a particular ingredient for an antidote from a place where it was not supposed to be taken. Dumbledore, seeing no other option, decides to steal it. His motive here is to save the school and its students, even if it means breaking the rules.
Sasuke might want to get some information from Naruko. Maybe he suspects that she knows something about a threat to the Uchiha clan that he is trying to uncover.
Well, in some fanfictions, Harry might attack Dumbledore if he discovers that Dumbledore has been using him as a pawn in a bigger game all along. This feeling of betrayal could drive him to lash out. Also, if there is a prophecy that he misinterprets to mean Dumbledore is a threat to his future or the future of his friends, that could be a motive.
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.
Maybe Rowle is under the orders of a more powerful dark wizard. In the world of Harry Potter, there are always those higher - ups in the dark side who might want Hermione for her knowledge of magic, especially things like ancient spells and magic theory. So Rowle could be tasked with kidnapping her for that purpose.
One possible motive could be to use Sakura as bait. Maybe Sasuke is trying to lure Naruto to a certain location. He knows Naruto cares deeply about Sakura, so he figures Naruto will come after her.
Aberforth Dumbledore can be a very important character in these fanfictions. He is Albus Dumbledore's brother and has his own feelings and history related to his brother and Grindelwald. He might be the one who tries to bring his brother back from the brink when Dumbledore is too involved with Grindelwald. Also, Leta Lestrange could be popular. Her family's dark reputation and her own complex relationship with Newt and the wizarding world in general can add an extra layer of drama to the fanfictions involving Dumbledore and Grindelwald.
It could also be a personal vendetta. Maybe she had some sort of conflict with someone in the past, and that person decided to kidnap her as revenge. For example, if she had testified against someone in a court case, the person might want to get back at her.
One possible motive could be for a prank. People might want to give their friends or family a big scare and then have a good laugh about it later. For example, like the stories where friends plan a fake abduction to surprise the victim with a party or some other fun event.