In actual classical reality, it's not at all meaningless to ask whether the cat is "dead or alive before looking". It might be uncertain, but it's not meaningless.
One might say "I think it's alive" and another "dead" -- and they have a chance to be right even before opening the box -- we'll just need to open it and see which was right ALL ALONG.
In quantum physics, on the other hand, in most interpretations, none of them is right before opening the box. If one says "the cat must be dead", and we open the box and the cat is indeed found dead, that person, wasn't right all along. He only became right upon the opening.
That's the whole paradox that Schrodinger tried to point out as an absurd result of quantum mechanics -- but which nonetheless is accepted by physicists not as a counter-example against QM, but as something still paradoxical that actually illustrates a key point about QM.
You're arguing against what one might call an objective Bayesianism stance. That is to say that our probabilities reflect our inadequate information concerning an objective (classical) state of reality for the cat.
However the phrase
> Schrodinger's cat is not both alive and dead. We know nothing about its current state, only how probable certain outcomes are
suggests a perspective in which there is not an objective (classical) state of reality for the cat. Rather, probabilities might be seen as subjective assertions about the outcome of interactions with the system. It is meaningless to talk about the cat being dead or alive before looking. This is closer to what one might call a subjective Bayesian stance.