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.
Perhaps Sasuke kidnaps Hinata out of jealousy. He might see her relationship with Naruto (if there is one in the fanfiction) as a threat to his own place in the ninja world or in Naruto's life. Sasuke has always had a complex relationship with Naruto, and Hinata could be caught in the middle. He could also be acting on behalf of someone else without fully realizing the implications. This could lead to a whole series of events where Hinata has to figure out how to escape or change Sasuke's mind, while Sasuke has to deal with the consequences of his actions.
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.
Maybe she's trying to protect Naruto from something she knows about but others don't. She might think that by kidnapping him, she can keep him safe from an imminent threat that the village or his friends are unaware of.
Maybe Sasuke is being manipulated by an evil force that wants to get at Naruto through Hinata. Since Hinata is important to Naruto, targeting her would be a way to hurt Naruto.
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.
At first, Hinata's reaction might be one of shock and disbelief. She has probably never expected Sasuke to do such a thing. However, she is a strong - willed character deep down. So, she might start to plan her escape. She could use her knowledge of the ninja world and her own family's techniques. She might also try to find out if Sasuke has any allies or if there are other forces at work. She could try to turn the situation around and make Sasuke realize that what he is doing is wrong by appealing to his better nature or by using her own skills to outwit him.
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.
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.
Well, in this kind of fanfiction, Doc Oc could kidnap Spiderman to force him to reveal his identity. Doc Oc might think that knowing who Spiderman really is would give him an upper hand in their ongoing battles. It could also be that Doc Oc wants to study Spiderman's powers. He's a scientist after all, and Spiderman's abilities are quite unique. He might believe that by kidnapping and examining Spiderman, he can find a way to replicate or counter those powers.
Well, in such a fanfiction, Itachi might kidnap Hinata for various reasons. Maybe he's being controlled by some dark force and needs Hinata for some ritual. Or perhaps he's been misinformed that Hinata has some special power that can help him in his secret mission against the Hidden Leaf Village.