“Back in the old days, when it rained people would put their cats and dogs up in the rafters so they would not get wet. [Variation: animals would climb up themselves to avoid the weather.] But the roofs often leaked, and the beams would get slippery so the animals fell, and it really was ‘raining cats and dogs’!”
There’s no myth here, just a question about the origins of this common saying. The best I can do is to report that a word search in JSTOR made me think the origin of the phrase may be Irish, as those are the earliest written usages I found. My opinion: this is a nonsensical phrase, like “raining pitchforks,” used to indicate severe rainfall and is not based on anything concrete.