YOU SAID:
It's raining rain, not cats or dogs.
INTO JAPANESE
雨が降り、猫や犬ではない。
BACK INTO ENGLISH
It started raining, in cats and dogs.
INTO JAPANESE
それは猫や犬で雨が降り始めました。
BACK INTO ENGLISH
It started to rain with cats and dogs.
INTO JAPANESE
猫と犬と雨が降り始めた。
BACK INTO ENGLISH
It began to rain cats and dogs.
INTO JAPANESE
雨が土砂降りに降り始めた。
BACK INTO ENGLISH
It began to rain cats and dogs.
That didn't even make that much sense in English.