According to Victor Reppert, William Hasker has argued that The mind, even though it is caused to exist by matter, exists independently of matter and can, for example, exercise free will in the agency libertarian sense. An entire chapter is devoted to this claim.
This is an interesting claim, of course. How is it that the mind is caused to exist by matter, and yet is independent of it? Independent, yet caused? Does Hasker tell us where the mind resides? Is it in the knee, or the heart, or the brain? Why should it be connected to the brain at all? And if it isn't located anywhere in particular, then can I borrow someone else's for a while? Can our minds visit China for a month? ;-)
Sam Harris had argued that we really don't even need brains at all if there is a mind. Why should we have a brain at all if we have a mind that makes decisons for us and provides us with consciousness? God doesn't need a brain to be conscious or to think, according to theistic beliefs. So why should we? And while having a brain is something that can be explained by the God-hypothesis, it isn't what we would expect at all. This difference makes all of the difference. The question we need to ask isn't whether the God hypothesis can explain something with a few added premises. The question rather, is whether this is what we would expect if there is a God!
Because we have a brain in the first place, we can have strokes which affect our "minds." Because we have a brain, someone with a crowbar can affect how we think forever by taking it across our heads. Why is that if we have minds? This is a serious problem that leads people to say we have no minds at all, since there is obvious causation in one direction.
While I personally cannot fully explain how the brain works, or even how it evolved, the above problems seem insurmountable to me when it comes to believing we have immaterial minds.