Meh. Today. Where did this phrase even come from? I did a quick Google investigation...
The likeliest explanation seems to be that cats and dogs as used in the phrase actually came from catbolts and dogbolts, referring to bolts used to fasten doors and timber respectively. The OED documents a phrase "Instead of thunderboltes shooteth nothing but dogboltes or catboltes” (G. Harvey) from 1592 that suggests a play on the -bolt similarity to thunderbolts that illustrated a rain so hard it was akin to having hardware coming down on you. N.E. Toke, writing in the early 20th century, noted that, at that time, “…‘dogbolts’ and ‘catbolts’ [were] terms still employed in provincial dialect to denote, respectively, the iron bolts for securing a door or gate, and the bolts for fastening together pieces of timber.”
Seems like a logical transition language-wise, although I wouldn't ever associate the impact of rain falling on me with metal pieces of hardware – even nails or screws. The Library of Congress claims the phrase stems from various literature references throughout history. The only etymological theory that seems to make sense with our current use of the phrase – when it's raining really hard out – is this one:
“Cats and dogs” may come from the Greek expression cata doxa, which means “contrary to experience or belief.” If it is raining cats and dogs, it is raining unusually or unbelievably hard.
Fine, I'll take it. Time to go to work and face the cats and dogs.