Ah, I see what you're misunderstanding. You're not thinking about the problem in the correct light.
If you start with the premise that computer science is math, of course you'll reach the conclusion that computer science is math. And that's why you're so surprised that anyone else can reach any other conclusion. But the issue is in your premise - that's what you need to re-examine.
The math portions of computer science are math - and the non math portions are not. Your argument is equivalent to saying that Europe is defined by the counties in that continent using GMT - and concluding "Of course Italy isn't in Europe!".
Parts of Computer Science (the theoretical parts) sit in formal science just like logic and math do. But parts of CS like applied CS don't. All of the hardware design and software falls into applied CS and eventually slides into pure engineering.
But CS also is more amorphous than many other disciplines. Parts of it almost touch up against behavioral science with its subfield of linguistics, and syntax and semantics of language. And a failure of CS over the past 50 years has been the utter lack of progress in empirical data around human modeling of computation. We still don't have any empirical framework for evaluating what languages or modeling approaches are more efficient than others, or even what makes a more efficient programing language. As a result that is stuck in alchemy and cargo culting.
Models of computation and information theory begin to intersect with the natural sciences n the realm of physics. Physicists begin to push up against what is computable by nature in a given region of space. And Quantum computation begins to redefine what the physical bounds are on computation.
Don't begin by looking at what math is - if you do then the only thing possible to conclude is that it's math . An informal definition you could begin with might be "The theory and application of tools (ie formal cs) and models (ie applied cs) that predict and explain behavior related to Computation"
How do you model the real world via computation? What are the limits of computation? How do you implement computation?
Computer Science is the study of all aspects of computation.
