As a child, I begged for pets (rats, mice, hamsters) and was never allowed. (I didn’t have a pet till my 20s.)
My mom said she worried enough about my brother and I and didn’t need somebody else to worry about. It didn’t matter that I was up to the challenge to care the potential pets myself.
It’s interesting; it’s the opposite message you got. Neither is great.
But somehow we both became loving, responsible dog mamas!
Lupin had 3 families before us and was estimated to be only a year and a half when we adopted him. There must be so many families treating pets the way your family did.