Well, Obito could be doing it out of revenge. He has a long - standing grudge against the Hidden Leaf Village. Naruto is seen as a symbol of hope in the village. So, by kidnapping him, Obito could be trying to strike a major blow to the village's morale and show that their so - called 'hope' can be easily taken away.
It could also be for power. Some evil shinobi might believe that by capturing Naruto and somehow extracting the Nine - Tails' power, they can become extremely powerful. They might have some sort of dark jutsu or experiment in mind that requires the power of the Nine - Tails which is sealed within Naruto.
Another motive could be revenge. Maybe some in Iwa still hold grudges against Konoha for past conflicts. Since Naruto is a prominent figure in Konoha, kidnapping him would be a way to strike back at the village. They might think that by harming Naruto, they can make Konoha suffer.
One possible motive could be power. Danzo was always obsessed with having power in Konoha. By experimenting on Naruto, who is the Jinchuriki of the Nine - Tails, he might have hoped to harness the power of the Tailed Beast in some way. Maybe he thought he could create a super - soldier or gain some unique abilities from Naruto's connection to the Nine - Tails.
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.
Perhaps in the fanfiction, there is a prophecy or a vision that Tsunade has seen which makes her think that Naruto needs to be in a certain place or situation for the greater good. And she is so desperate to fulfill this that she resorts to kidnapping Naruto. This could lead to a story where Naruto initially resists but then comes to understand Tsunade's reasons as the story progresses.
Another motive could be related to her family. Maybe there was some sort of blood feud or an old grudge against the Grangers. The kidnappers could have thought that by taking Hermione, they could get revenge on her family. In some fanfictions, there are secret magical families that have long - standing rivalries, and Hermione's kidnapping could be part of that.
Another reason might be revenge. There could be a character who has a grudge against Inuyasha or someone close to him. So, they kidnap him to make him suffer or to use him as bait to draw out his friends. For example, if there was a demon whose family was slain by Inuyasha in the past, they might kidnap him for revenge.
One possible motive could be to use Sakura as a bargaining chip. If he has some sort of plan against Naruto or the Hidden Leaf Village, Sakura, being a close comrade of Naruto, could be very useful. He might think that by restraining her, he can force Naruto to come to a certain location or make concessions.
It might be an exploration of the 'nature vs. nurture' concept. Writers could be interested in seeing how Naruto's character would develop if he had a negative influence like an abusive Minato instead of the loving father he was supposed to have. Also, some might do it just to be different from the mainstream fanfictions and explore a more edgy side of the Naruto universe.
One possible motive could be to gain control over Naruto's power. Since Naruto has the Nine - Tails within him, Danzo might want to use that power for his own political or military gains. He's always been power - hungry and sees Naruto as a tool to achieve his goals of making Konoha stronger in his own way, which might involve more underhanded and controlling methods.