Well, in some fanfictions, it might be about protection in a very twisted way. Peter might think that the world around Stiles is too dangerous, and by kidnapping him, he can keep Stiles safe in his own lair. However, this is a very warped sense of protection, but it's a common trope in some darker fanfictions.
It could also be for revenge. Perhaps Stiles or someone associated with him has wronged Peter in the past within the context of the fanfiction story. So, Peter kidnaps Stiles to get back at him or those related to him. Another reason might be that Peter is being controlled by some other force. There could be a dark entity manipulating Peter's actions, and it makes him kidnap Stiles for its own sinister purposes.
It could also be for power. Perhaps Stiles has some knowledge or ability that Theo wants to use for his own gain. In the show, Stiles was quite smart and resourceful, so Theo might kidnap him to get access to that intelligence or those skills. In some fanfictions, Theo might be trying to use Stiles as a bargaining chip to get something from the other characters like Scott or Derek.
On the other hand, Stiles is also known for his quick thinking. He might start to try and bargain with Peter. He could offer to help Peter in some way if Peter lets him go. For example, if there's a problem in the supernatural community that Peter is facing, Stiles could say he'll use his human ingenuity to solve it. Also, Stiles could be angry. He might start shouting at Peter, calling him out on his actions, and trying to make Peter see how wrong this is.
One possible motive could be to force Naruto to understand his own power. Sasuke might think that by kidnapping Naruto, he can push Naruto to a situation where he has to tap into his full potential. Maybe Sasuke feels that Naruto has been relying too much on his friends and needs this shock to grow stronger on his own.
It could also be a matter of desperation. Perhaps there is a threat to the village or someone she loves dearly, and she believes that Naruto holds the key to solving the problem. But instead of asking him directly, she kidnaps him in a hasty and ill - conceived plan. This could lead to a lot of drama and character development as Naruto tries to understand her actions and they both work towards resolving the real issue.
One possible motive could be that in the fanfiction, Adrien is being controlled by some dark magic or an evil force. This external influence makes him act against his true nature and kidnap Marinette. For example, perhaps a villain has cast a spell on him to use him as a tool to get to Marinette, who might have some special power or knowledge that the villain desires.
In this fanfiction, Kate might be working for a greater evil. She kidnaps Stiles to force him to do her bidding. Maybe she needs him to break into a secure location or decrypt some important information. Since Stiles is often portrayed as clever, she might think he can solve a problem for her.
Perhaps Fleur is being controlled or influenced by a dark force. In the Harry Potter universe, there are many dark magic entities that could manipulate someone into kidnapping Harry. It could be that she is under the Imperius Curse or some other form of mind control. Another reason could be that she has some sort of personal vendetta against Harry or those close to him, and kidnapping him is her way of getting revenge. She might think that Harry has wronged her in some way, whether it's real or just in her deluded perception.
One possible motive could be Damon's possessiveness. In the 'The Vampire Diaries' universe, Damon has a complex relationship with Elena. He might kidnap her out of fear of losing her to someone else, like Stefan. Maybe he thinks that by taking her away, he can have her all to himself and make her see that he is the one she should be with.
One possible motive could be related to power. Maybe Sasuke thinks that Hinata has some sort of connection or knowledge that could help him gain more power. For example, her Byakugan might be of interest to him in terms of seeing things that he couldn't otherwise. Another motive could be a misdirected sense of revenge. He might believe that Hinata is somehow connected to someone he wants to get back at. It could also be a plot by an outside force that is controlling Sasuke to kidnap Hinata, perhaps for some kind of experiment due to her unique abilities.
Well, perhaps Stiles gets used as a bargaining chip against his friends. The alpha pack might want something from Scott or the others, and they think Stiles is an easy target to control them.