Christians in medieval and pre-modern Europe believed that Satan was a real being and that Satan was actively involved in the affairs of humans. Satan's goal was the corruption of humanity, the destruction of everything good, and the damnation of as many people as possible in hell. One means by which it was believed he accomplished this was through human agents to whom he gave supernatural powers.
Witches were easily categorized as servants of Satan. No longer merely adherents to a more ancient religious tradition, witches were targeted for prosecution as slaves of the cosmic enemy of God, Jesus, and Christianity. Instead of a healer or a teacher, the witch was made into an instrument of evil. The witch was portrayed -- and treated -- as worse than a heretic. This tactic was not limited to the medieval church's pursuit of witches.
Religious and political authorities of various eras and different cultures have always found it convenient to associate their enemies with the worst possible evil they could imagine. In the Christian west, this generally meant associating enemies with Satan. These sort of extreme demonization allows a person to stop seeing their enemy as entirely human and the conflict as something which does not require mercy, traditionally just procedures, or anything of the kind. The only just outcome is not merely the defeat the one's enemy, but their complete extermination. In a battle where one's very existence is at stake, survival becomes the only moral value worth upholding.
The above image depicts the "Witch's Kiss." It was believe that part of the rite of becoming a witch in Satan's service involved kissing Satan's rear. It should be remembered that insofar as there existed anyone who practiced the healing and divination techniques of older pagan traditions, they wouldn't have had anything to do with Satan. After all, Satan is a creation of Christianity and monotheistic traditions. Any "witches" who existed were pantheists or polytheists and wouldn't have believed in a Satan.