YOU SAID:
I like to pet my cat.
INTO JAPANESE
私は私の猫を飼うのが好きです。
BACK INTO ENGLISH
I like to keep my cat.
INTO JAPANESE
私は猫を飼いたい。
BACK INTO ENGLISH
I want to keep a cat.
INTO JAPANESE
私は猫を飼いたい。
BACK INTO ENGLISH
I want to keep a cat.
That didn't even make that much sense in English.