I am not an expert on this, but a couple things come to mind, and both have to do with passages in the bible. The first is the dividing of sheep and goats in Revelations. The goats are the ones sent to hell, nominally for not doing good to the poor. I don't know why the author of Revelations associated that with goats.

The second is the original "scapegoat". It was an actual goat (or at least, was in the story in Leviticus). The idea of a scapegoat is, if not universal in early religions, then certainly very common. It was something that absorbed the sins and evils of a community and died or was exiled for it. In many places it was beggars or animals of some kind; in Leviticus, it's a goat. I'm not sure if there's a reason early Judaism settled on a goat to be their scapegoat, besides the fact that that's what they had in their herds. But if it'd been a cow, we'd now have scapecows instead of scapegoats.

So, that doesn't really explain why our cultural ancestors had a thing against goats. Really, they probably didn't, at least not very much. Herding goats was a very common living. But hopefully it does explain the origins of our association between goats and bad things. And hopefully someone else will come along and do a better job explaining.

Sorry, can you clarify in what context you see a goat used to symbolise evil or sin? That would help me answer your question instead of throwing up random facts about goats in religions.