The counter to that is that altering the brain directly alters the consciousness. I can take LSD and I literally change. I can have parts of my brain removed and parts of my self disappear. It's not like cutting off a leg, where I lose capabilities but am still the same me.
The logical conclusion is that the brain makes me.
> The logical conclusion is that the brain makes me
The logical conclusion under the popular axiomatic framework of materialism, for sure.
But there are other possible logical conclusions depending on your philosophical foundations, e.g. the brain could be a receiver for consciousness which is translated into our worldly experience from somewhere else.