Смотрим на одном сайте:
Take (please!) this electronic explanation of a common meterological phrase: "Houses had thatched roofs. Thick straw, piled high, with no wood underneath. It was the only place for animals to get warm, so all the pets -- dogs, cats, mice, rats and bugs -- lived in the roof. When it rained it became slippery and sometimes the animals would slip and fall off the roof. Hence the saying, 'It's raining cats and dogs.'"

Dubious. The literal explanation is that during heavy rains in not so Merry Olde England some city streets became raging rivers of filth carrying many dead cats and dogs. But there is also strong evidence that the phrase "it's raining cats and dogs" may not be literal.

In the dark Ages, people believed that animals, including cats and dogs, had magical powers. Cats were associated with storms, especially the black cats of witches, while dogs were frequently associated with winds. The Norse storm god Odin was frequently shown surrounded by dogs and wolves. So when a particularly violent storm came along, people would say "It's raining cats and dogs," with the cats symbolizing the rain and the dogs representing the wind and storm. This folkloric explanation is supported by such expressions as "it's raining dogs and polecats" and "it's raining pitchforks."

Смотрим на другом:
A case in point is the “theory,” according to which the source of it is raining cats and dogs is Nordic. Allegedly, in Norse mythology cats were supposed to have great influence on the weather, while dogs were a signal of the wind; or cats were a symbol of heavy rain (whatever symbol means here), while the dog, an attendant of Odin, the storm god, represented great blasts of wind; or witches in the guise of cats rode upon the storm and followed Odin and his dog. A theory indeed. In Norse mythology, Odin is not a storm god, his “animals” are a horse and two ravens, cats have nothing to do with either Odin or witches, and rain is not connected with any divinity. Odin presides over the Wild Hunt in late Scandinavian folklore, not mythology. The Wild Hunt, which is known in most of northern Europe, is obviously associated with stormy weather, but Odin’s following is made up of flying corpses, not of cats, dogs, or witches. Under no circumstances can the English idiom be traced to any scene in Scandinavian oral tradition.

На твоей любимой Википедии:
Unknown. Perhaps from the Latin cata doxus (contrary to experience), or from cases where small fish, frogs, etc. have been reported to be deposited in rainstorms.

Еще раз на другом:
The idea that it is raining cats and dogs is an alteration (“corruption,” as people preferred to say in the 19th century) of some foreign phrase has occurred to many. The Greek phrase kata doksa, approximately, “contrary to expectation” (compare Engl. cataclysm, and orthodoxy) seemed especially worthy of note because even in Modern Greek one sometimes uses it in describing a downpour, and the same phrase has reportedly been heard from Gypsies (in what country?). But in Greek (assuming the information is reliable), kata doksa can be applied to any phenomenon that is unexpected. Before we go on, an additional point should be made. When borrowing is suggested, reference to a similar-sounding word or phrase in a foreign language is not enough, for the ways of reaching a new home have to be traced. How did Greek kata doksa make its way into English? Did the English phrase originate among university wits (not an uncommon situation), or did it have popular origins? Unless evidence exists that it is raining cats and dogs first had some popularity at Oxford or Cambridge, the Greek hypothesis, not unlike the cats and dogs themselves, falls to the ground.

Короче,никто нихера не знает откуда взялась эта фраза.Теория Акифыча наиболее правдоподобна,ибо наиболее часто встречается и объяснение вполнне логично(опять же Houses had thatched roofs. Thick straw, piled high, with no wood underneath. It was the only place for animals to get warm, so all the pets -- dogs, cats, mice, rats and bugs -- lived in the roof. When it rained it became slippery and sometimes the animals would slip and fall off the roof. Hence the saying, 'It's raining cats and dogs).Но это все интернет.Ему доверять опасно,но некоторые выводы сделать можно. Точно тебе никто не скажет.Любая более или менее обоснованная теория имеет право на сущесствование.