Another aspect could be that Dumbledore is being controlled or influenced by some external force. In the fanfiction, this could lead to a very interesting story where Harry has to figure out how to break Dumbledore free from this control while also escaping from his 'kidnapper'. It would be a total role - reversal from the original story.
In this kind of fanfiction, it could be that Dumbledore has some very complex motives for 'kidnapping' Harry. Maybe he wants to protect Harry from a danger that he can't explain openly. For example, there might be a powerful dark wizard who has found a way to spy on Hogwarts and Dumbledore believes that keeping Harry in a secret location is the only way to keep him safe.
At first, Harry would be in shock. He would be full of disbelief that Dumbledore, of all people, would do such a thing. He would struggle both physically and emotionally. Physically, he would try to break free from whatever bindings or magical restraints Dumbledore has put on him. Emotionally, he would be a mess, feeling hurt, scared, and confused. However, depending on how the story unfolds, he could gradually come to terms with the situation if Dumbledore manages to convince him that it's all for a greater good.
Often in fanfiction, the idea that it wasn't Harry Potter's fault can be a way to rewrite parts of the story. For instance, in some fanfics, Harry might be wrongly accused of using dark magic when in fact he was set up. This allows the writer to create new plotlines, like how he clears his name and uncovers the real culprit. It gives a fresh perspective on the Harry Potter universe.
Fanfiction often creates alternate scenarios. It could be that Dumbledore has a hidden agenda that Harry uncovers, which goes against Harry's sense of right and wrong. Maybe Dumbledore is trying to sacrifice Harry in a way that Harry doesn't agree with, leading to their opposition. This can be a very creative way to rewrite the dynamics between the two characters.
Perhaps in this fanfiction, Dumbledore has a secret plan related to Harry's power. He might think that by kidnapping Harry, he can train him in isolation to fully develop his magical abilities without the distractions and potential dangers at Hogwarts. It could also be that Dumbledore is trying to hide Harry from Voldemort in a way that no one would suspect, as Voldemort would never think Dumbledore would use such extreme measures against Harry.
Well, perhaps Dumbledore has some dark secret and believes Harry is the key to it. He might kidnap Harry to keep him away from Voldemort in a very unorthodox way. Maybe he wants to train Harry in isolation for some super - powerful magic that he doesn't want Voldemort to find out about.
One reason could be to add a new twist to the story. Fanfic authors might want to make the familiar character of Dumbledore more unpredictable. Another reason might be to explore the idea of power corrupting. Since Dumbledore had a great deal of power, showing him as insane could be a way to show how that power might have affected his mind over time.
At first, Harry may be in shock. He's been taken by someone he respects and looks up to. As he comes to terms with his situation, he might try to reason with Dumbledore. If that doesn't work, he could start to plan an escape, using his wits and the magic he knows. He might also feel angry that Dumbledore is treating him this way when he's always been on Harry's side, or at least that's what Harry thought.
Well, in certain Harry Potter fanfiction, Dumbledore can come across as insane. It really depends on the writer's interpretation and the direction they want to take the story. Some might do it for shock value, to create a more edgy or different take on the well - known character. However, the canonical Dumbledore was a highly intelligent and calculating figure, not insane.
Well, Harry might outsmart Dumbledore by using his unique understanding of the magical world in ways Dumbledore doesn't expect. For example, Harry has a more direct experience with some dark magic items due to his encounters with Voldemort. He could use this knowledge to make decisions that seem counter - intuitive to Dumbledore but are actually more effective in a particular situation.