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.
It could also be a case of mistaken identity. Some other powerful force might be after a different half - demon with similar powers as Inuyasha. And in the chaos of the situation, they end up kidnapping Inuyasha instead. This could lead to all sorts of comical or dangerous situations as Inuyasha tries to convince them of their mistake.