why is satan a half goat
goats = bad is a pretty old trope within Christian discourse,
it's in the New Testament. Goats in general held religious currency with a fair amount of peoples in the ancient Levant and its environs, to Jews in the Old Testament they're primarily shown in the context of sacrificial offerings, so if I had to speculate I'd say the association with Satan/hellfire doesn't happen until later. The concept of Satan as a physical being materializes in the west around the 5th-6th century A.D., imagery that we'd be familiar with is evidenced on
Muiredach's High Cross which dates to the 9th-10th century;
Goya would be able to depict Satan as a goat in the
late 18th. The name Baphomet is first documented in the late 11th, and for the next ~300 years is only brought up in the context of heretical inquisition, probably most famously in the case of the French Knights Templar. early western estoericists like Eliphas Levi and Aleister Crowley appropriated this imagery + the use of Baphomet in the 19th, LaVey in turn appropriated this aesthetic and retooled esotericism into something of a formal organization of Satanism in the 60s. It's primarily from the last 2 developments that Satan gets his conceptualization in the modern imagination.