I think the language of "soul" for that ineffable metaphysical quality is going to set some teeth on edge (as it already has), so let's recast the same essential point but actually take into account Occam's Razor, shall we?
Now, obviously the brain is a physical, biological thing ruled by physical and biological forces. Emotions, such as love and the like, happen concurrently with certain kinds of chemical swells. Most every aspect of human consciousness has been linked to activity in the brain, and I only say "most" because someone, somewhere, could get nit-picky and say "But we don't know what section lights up when contemplating the Gamma Function" or some such crap.
Now, the argument for the soul comes from the (basically valid) observation that physical processes alone don't explain our subjective consciousness. That is, why do we experience our own consciousness in specifically the manner we do?
A metaphysician is likely going to answer that there is some "ineffable soul" attached to the body which experiences/governs these "higher" experiences of consciousness. But that is not a necessary assumption. A mechanist will argue that the biological mechanisms of the brain do, indeed, account for all of that. It requires a bizarre kind of conceptual leap to see how this is the case, but it can be (though doesn't have to be) argued as such: if we let all physical actions be SIMULTANEOUSLY metaphysical actions (without a causal link in either direction--it's literally the same thing), the metaphysical action of the biological processes of the brain is, indeed, consciousness. A quick argument against this is a simply denial that physical actions are equally metaphysical, but at a very basic level, I ask the respondant to find, for me, a physical action that is not also an information motion. Information is inherently metaphysical (or epistemological, depending on its domain).
What this demonstrates is that a SOUL, as such, in some ineffable sense, is not necessary. But what IS necessary is SOME link between the physical brain and the metaphysical mind. But that link doesn't have to be mystical or any such thing. It can, indeed, probably even be understood scientifically (Information Theory is rapidly developing as a scientific and philosophical field).