Why does it make sense that the term "tragedy" comes from the Greek word for "goat"?

It is said that the term tragedy was a contracted word of Classical Greek trag (o) - aoidia = "goat song". Originally from tragos = "he-goat" and aeidien = "to sing".

Tragedy was associated with goats because during the Classical Greek, Choral dancing was a competition and a live goat is its prize.