On one side of the debate are those who argue that thoughts are not physical, and therefore cannot be generated by something physical. Apart from obvious religious and soteriological reasons, one of the more popular lines of argument goes roughly as follows: when we have a complete physical description of the brain (and of that which is perceived by the brain), there is still something about the qualitative nature of first-person subjective experiences (or qualia) that is not accounted for, so there must be something non-physical to explain this. In other words, the physicalist account leaves something rather important out of the picture, namely subjectivity and intentionality (or the 'aboutness' of mental experience), and that needs to be explained.
On the other side, the idea of an immaterial soul seems perhaps even more mysterious than the problems with physicalism: how can a non-physical substance interact causally with the physical body? What is it about this non-physical stuff that allows it to think and have first-person subjective experiences in the first place, without just being defined into having it? How can we possibly verify its existence (without arguing in a circle)? In fact, the evidence that we do have when we study the brain, especially when it suffers damage that affects very specific cognitive capacities, seems to indicate that even though we may not know the exact mechanism through which brain processes produce consciousness, that's nevertheless what happens.
But why listen to me when we have a beautiful and nicely organized animation that will take you through the steps to analyze this debate?
Did I say a beautiful animation? I meant two :)
Isn't it amazing how many problems fade away when you organize your thoughts? :)