Note that Schrödinger's thought experiment is intended to ridicule this way of thinking. Schrödinger is trying to suggest that since it's clearly nonsensical to imagine that maybe a whole cat can be both dead and alive the same would be true for other macroscopic subjects.

Instead popular culture has decided that at best, this is what Schrödinger believed (Ha those crazy scientists) and at worst that somehow the cats being dead and not-dead at the same time is the core idea of quantum physics :/