The issue is not whether the brain is necessary for consciousness, but whether it is sufficient. Like you said, brain damage affects our conscious experience. However, consciousness includes a purely subjective element that, so far, has no explanation in a reductionist sense. That is, why do we experience redness? Why is there an experienced inner life?
Science is a great tool for explaining how the brain works, in the sense of "why did I do that?" or "how are signals from the optical nerve processed?". However, because the experience of consciousness is so subjective, I doubt that science will be able to explain it. After all, science is designed to work on objective reality.
> ...because the experience of consciousness is so subjective, I doubt that science will be able to explain it. After all, science is designed to work on objective reality
The experience is subjective. But what are the actual details that produce that experience? We just don't know. But if it has an explanation there is no reason to presume that that explanation must have the same sorts of properties as what is being explained.
An analogy: before we understood what is actually going on with fire (a kind of molecular reaction), it could seem as if it was a separate category of stuff - what else was there that was like fire? But it would have been wrong to assume that therefore "fireness" was some fundamental, intrinsic property of fire.
As to subjective conscious experience, we don't know what it is, and I don't think there's any reason to think that the explanation will itself be 'subjective', and that it can't be something objective (even if it's some different kind of objective detail, different from anything else we currently understand).
Science is a great tool for explaining how the brain works, in the sense of "why did I do that?" or "how are signals from the optical nerve processed?". However, because the experience of consciousness is so subjective, I doubt that science will be able to explain it. After all, science is designed to work on objective reality.