But quantum cats don’t follow those rules. A quantum cat does everything — chasing its tail, sleeping, stretching, eating — all at the same time. It has no fixed location; it manages to be everywhere at once. Only when we measure the cat in some way — even simply by looking at it — is it forced into a particular activity and place.
I think this was not the takeaway from Schrodinger's thought experiment. The idea was to show that the radio active material obeying rules of quantum mechanics has a probability of either killing the cat or not. The cat itself is not quantum, and does not superposition itself.