His motives could be related to protecting the wizarding world's secrets. Hermione is very intelligent and curious. Dumbledore might fear that she will uncover some dark secrets that are better left buried. So, in order to keep those secrets, he betrays her, perhaps by framing her for a crime she didn't commit to keep her away from certain areas or investigations.
Dumbledore might be motivated by his over - arching plan to defeat Voldemort. He could see Hermione as a sacrifice that needs to be made. Maybe he believes that by betraying her, he can gain some crucial information from the enemy that will ultimately lead to Voldemort's downfall.
It could also be that Dumbledore has some secrets that he's afraid Hermione will uncover if she's left to her own devices. Hermione is known for her inquisitive nature. So, to keep these secrets hidden, he attempts to control her. For instance, if there are some hidden aspects of Hogwarts' history or certain faculty members that he doesn't want exposed, he might use control over Hermione to prevent her from delving too deep.
One way it could develop is if Dumbledore withholds important information from Hermione about her family or her own magical abilities. He might do this because he fears she will use that knowledge in a way that could disrupt his grand plan for the wizarding world. For instance, Hermione discovers she has a special power that could defeat Voldemort easily, but Dumbledore has kept it from her all along, making her feel extremely betrayed as she could have saved many lives if she knew earlier.
One possible motive could be for Harry's protection. Dumbledore might have seen a threat that Harry wasn't aware of, and he asked Hermione to keep an eye on him. Hermione, being the loyal friend and also having great respect for Dumbledore, would have agreed to it.
In this fanfiction scenario, Dumbledore could be acting out of desperation. He may have seen a future where Harry is in great danger and the normal means of protection within Hogwarts are no longer sufficient. So, he resorts to kidnapping Harry. It could also be related to some secrets about Harry's family or his own power that Dumbledore has been keeping. He might think that by taking Harry away, he can finally reveal these secrets to him in a controlled environment and train him better for the upcoming battles.
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.
If such a fanfiction exists, perhaps the motive could be a misdirected attempt at protecting the greater good. Maybe Dumbledore thought Hermione's parents were in some way a threat to the wizarding world's secrets that he was trying so hard to protect. But this is still a very far - fetched idea as Dumbledore was always about protecting life in the official story.
In a more extreme case in the fanfiction, Dumbledore might assign Hermione to a special project that is both difficult and dangerous as a form of punishment. For example, he could send her to study a group of cursed magical creatures in the Forbidden Forest. This would be a punishment that not only tests her skills but also her courage.
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.
One possible motive could be a misguided sense of protection. Dumbledore might think that taking something from Harry, like a powerful magical item, would keep it out of the wrong hands. He may believe that Harry is too young or inexperienced to handle it properly.
One possible motive could be protection. Dumbledore might tie Harry to the bed to keep him from running off into danger. He has always been protective of Harry and perhaps in this fanfiction's unique scenario, he believes this extreme measure is necessary to safeguard Harry from some immediate and unseen threat.