Quantum mechanics is more weird than that. It's not accurate to say things can be in two states at once, like a cat that is both dead and alive at the same time, or a qubit that is both 0 and 1 at the same time. If that were true, then the qubit's mathematical description when in a superposition of states would be |0>+|1>, but it is not, it is a|0>+b|1> where the coefficients (a and b) are neither 0 or 1, and the coefficients cannot just be ignored if one were to give a physical interpretation as they are necessary for the system's dynamics.

You talk about it being "half" a cat, so you might think the coefficients should be interpreted as proportions, but proportions are such that 0≤x≤1 and ∑x=1. But in quantum mechanics, the coefficients can be negative and even imaginary, and do not have to sum to 1. You can have 1/√2|0>-i/√2|1> as a valid superposition of states for a qubit. It does not make sense to interpret -i/√2 as a "half," so you cannot meaningfully interpret the coefficients as a proportion.

Trying to actually interpret these quantum states ontologically is a nightmare and personally I recommend against even trying, as you will just confuse yourself, and any time you think you come up with something that makes sense, you will later find that it is wrong.