It could be a deranged fan of one of Reid's academic works. This person might have misinterpreted Reid's theories and decided that Reid was some sort of false prophet. So, in his twisted mind, he kidnaps Reid to 'correct' him.
Perhaps a new unsub who is obsessed with power and knowledge. He sees Reid as a source of both. He kidnaps Reid to force him to share his vast knowledge, and if Reid refuses, he threatens to harm Reid's loved ones at the BAU.
It could be someone Reid put away in the past. Maybe a criminal who has held a grudge against him ever since and has now found an opportunity to kidnap him for revenge.
One possible motive could be revenge. Maybe Reid has put away a relative or someone close to the kidnapper in the past. Another motive might be related to Reid's intelligence. The kidnapper could want to use his brainpower for some illegal or self - serving scheme, like cracking a code or coming up with a complex plan.
It could be a disgruntled former crew member. Maybe they were fired from the show and in their anger, they read a lot of fanfiction for inspiration on how to get back at the team. So they plan and execute the kidnapping.
It could be a copycat unsub who idolizes the previous criminals the BAU has caught. He might have studied Reid's work and decided to target him to make a name for himself in the criminal world.
One great Reid kidnapped fanfiction is 'The Abduction of Reid' on FanFiction.net. It has an interesting plot where Reid is kidnapped by an unsub with a personal vendetta. The author does a great job of building suspense and keeping the characters in - character.
Maybe it's a cult leader. The cult might believe that Reid has some sort of special knowledge or power that they want to harness. They kidnap him to convert him to their beliefs or use his mind for their own strange purposes.
Another theme is Reid's own personal growth during the ordeal. He may face his fears, or learn something new about himself. For example, in some fanfictions, he discovers a new level of strength or resilience that he didn't know he had while being kidnapped.
Often, these fanfics can be a great way to expand on the relationships within the Criminal Minds universe. When Reid is kidnapped, it could bring out different sides of his relationships with his colleagues, like the deep - rooted loyalty and friendship they have for him.
Perhaps it's an organization that wants to use Kakashi for their own evil plans. They might think that Kakashi's skills and knowledge would be useful for them. For example, they could be trying to create some sort of super - weapon and they need Kakashi's expertise in ninjutsu.
It could be Hades. He's always been an antagonist in the series and might kidnap Pit to mess with the gods. He could be thinking that by taking Pit, he can gain an advantage in his ongoing feud with them.