The goat has been a potent symbol in European folklore for a long time. Goats were the beasts that hauled Thor's chariot, and the goat was important to the Greek goddess, Hera, and it played role in the cult/stories of Athena, Artemis, and Aphrodite. For the Romans, Dionysus could assume the form of a goat, and as the Fung and Wagnall's, Standard Dictionary of Folklore (1949, p. 456) suggests, "Pan, the fauns, and satyrs have goat (or goatlike) bodies."

This final association - combined with the perceived hyper-sexuality of Pan, the fauns, and satyrs - put a Christian target on the back of the goat. Conversion was an uneven and gradual process, so it was not uncommon for people to consider themselves to be Christians while innocently maintaining pre-conversions beliefs and devotional practices. All this created a situation where Christian priests could make the case that pre-conversion associations of the goat meant that Satan himself was associated with and often appeared in the form of a goat.

A deleted post in answer to this question addressed some biblical references to goats that I am not in a position to replicate (some of the observations had merit). One observation needs to be refuted entirely, namely that Viking horns were an erroneous attempt by Christians to place goat's horns onto the helmets of Vikings, the perceived demonic enemies of their faith. Viking horns were NOT those of goats - they were typically bull horns according to the erroneous association of Vikings with horned helmets. In an effort to put forward a better analysis of the question of the origin of this very-late motif, I put forward the following question, asking for insight into how Vikings became incorrectly associated with horned helmets. But for anyone who read the deleted post, let's put to rest any association of Vikings with goat horns.