It's amazing that the US government has, in some capacity, issued an official statement on the etymology of "it's raining cats and dogs". According to the library of Congress website, the first usage was in a 1561 collection of poems by Henry Vaughan. It subsequently racked up more attestations, eventually used by Jonathan Swift and going as viral as you could back in those days. But why did Vaughan say "cats and dogs"? Nobody knows for sure, but there are some theories. The most widely accepted origin is that it comes from Norse mythology, when cats were associated with wind and dogs were associated with rain- so, metaphorically speaking, when it's "raining cats and dogs", it's "raining wind and rain". Another etymology, although not as likely, is that this could be a corruption of the Greek phrase cata doxa, meaning something like "unbelievable" "unexpected"- so it implies that the storm is surprisingly strong. There's also a myth that the phrase comes from when cats and dogs cuddled in thatched roofs during storms in the Middle Ages and got washed out, although that's completely bogus.
Adam Aleksic, a rising sophomore studying linguistics and government at Harvard University, has been described as the internet's sixth most famous etymologist. He also has disturbing interests in politics, vexillology, geography, board games, conlanging, and law.