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.