I think the biggest counterargument (if one were needed) is that if I start doing things to your brain, it affects your mind. If I cut a part of your brain out, your mind is impacted. This has been shown by injuries to the brain, lobotomies, etc. etc.

Beyond that, we could get into all sorts of philosophical arguments about the link between the mind and the brain, but it seems to me as a somewhat philosophically naive person that this fact is a clear and demonstrable link between the brain and the mind.