There could also be some humans who are under the influence of dark magic or who have a vendetta against Inuyasha. Maybe they were promised great power by a demon in exchange for kidnapping Inuyasha. Or perhaps they blame Inuyasha for some misfortune that befell their village, like a famine or a disease that they wrongly think Inuyasha caused.
The Naraku would be a likely kidnapper. He is always plotting against Inuyasha and trying to get his hands on the Tessaiga. Kidnapping Inuyasha would be a way for him to either steal the sword or find a way to break Inuyasha's spirit so that he can no longer oppose him.
Some other powerful demons who see Inuyasha as a threat might also be the kidnappers. For instance, a demon who wants to be the sole ruler of the demon world might think that by getting rid of Inuyasha, he can achieve his goal more easily. So, they would kidnap him to either kill him or keep him out of the way.