One possible motive could be Severus' complex relationship with Harry's father, James. Maybe Severus feels a deep - seated resentment towards James and by kidnapping Harry, he wants to get some form of revenge on the Potter family. Another motive could be related to the war. He might think that by having Harry in his custody, he can use Harry as a bargaining chip either with Voldemort or the Order of the Phoenix. He could also believe that he can protect Harry better than others, in his own, rather extreme way, thinking that others in the wizarding world are not capable or trustworthy enough to keep Harry safe.
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.
Well, his motive might be related to his twisted sense of love. In the context of fanfiction, Hannibal could think that by kidnapping Will, he is protecting him. He may view the world as a dangerous place for Will, and his actions are a way to keep Will safe in his own, very abnormal way. Also, it could be a power play. He wants to show that he has the power to take Will whenever he wants, asserting his dominance over Will.
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.
One possible plot could be that Fleur has been influenced by some dark magic or a powerful enemy. Maybe she's being blackmailed to kidnap Harry. She might take him to a hidden location, perhaps an old, abandoned castle. Then, the story could revolve around Harry trying to figure out why Fleur did this and how to escape while also dealing with Fleur's internal struggle about what she's done.
It could be that Lucius is under the orders of Voldemort. Voldemort wants Harry alive but in his control, so he sends Lucius to kidnap Harry. Lucius might then keep Harry in some secret location, perhaps an old Malfoy manor cellar, guarded by dark magic spells. Harry would then have to find a way to escape, maybe by using his own unique magic abilities or with the help of his friends who eventually figure out where he is.
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.
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.