Chalmers posits that the non-physical mental properties parallel the information processing properties of the system. But if they parallel them perfectly, and thus explain the mind, why not just identify them? ... the dualist explanation posits something more than the materialist version of the same theory does: it must posit additional laws governing a new domain of mental stuff that makes it behave in this way and stick to the right sort of physical systems.
On the other hand, the (type B) materialist theory posits ad hoc 'strong necessities', which we have no independent reason to believe in. (Kripke's "necessary a posteriori" is no help.)
Consider the question: why aren't we non-conscious zombies, mere hunks of matter that exhibit complex behaviour without any "lights" on inside? The materialist answers that zombies are impossible; that consciousness is nothing above and beyond the complex arrangements of matter that our bodies (brains) comprise. But this strikes me as an unsatisfying explanation, that doesn't really do justice to the phenomena.
The dualist can do better. She may acknowledge the depth of the problem -- that consciousness is something new, something that goes beyond merely material properties. She can also acknowledge the modal fact that zombies (non-conscious physical duplicates of ourselves) are possible. So, rather than merely rebuffing the question "why aren't we zombies?" as empty or ill-formed, the dualist takes it seriously, and offers an answer:
The reason we're not zombies is because of the contingent natural laws that govern our universe. There are psycho-physical bridging laws, which ensure that matter gives rise to consciousness. (Note how intuitive this claim is: we think that consciousness emerges from the brain; not that it just is the brain!) The zombie world has no such bridging laws. Its laws are merely physical, so that brains and other matter causally interact without giving rise to genuine consciousness in addition. That's the difference.
Materialists can't explain this difference, because they don't take the zombie intuition seriously. Once the brain matter is there, they think that's all there is to consciousness -- there's nothing further to explain. Most of us think there is something still to be explained, and dualism can achieve this by positing bridging laws that cause 'mind' to emerge from 'matter'.
Even dualists can agree that in our world (i.e. given the actual laws of nature) complex brain states suffice for consciousness. The briding laws make zombies nomologically impossible. And that's all science is concerned with. As philosophers, though, we're interested in a broader sense of possibility, in which we can't just take the natural laws for granted. So, once our familiar psycho-physical bridging laws are taken away, we should ask: does matter alone suffice for consciousness? The zombie world demonstrates that the answer is no. Take away the bridging laws, and our physical stuff might no longer give rise to any conscious experiences.
In summary, it's worth emphasizing three points:
(1) Materialism - perhaps surprisingly - turns out to be theoretically extravagant, due to its modal ambitions. It posits 'strong necessities', which we have no independent reason to grant, and indeed goes against everything else we know in philosophy. Dualism is thus the more philosophically modest theory.
(2) Additional laws are worth positing, to explain why we're conscious rather than zombies. (The unsatisfying alternative is to merely dismiss the question.)
(3) Contrary to popular belief, dualism need not be in tension with science. It only diverges from materialism in its extra-nomological implications -- i.e. matters that concern philosophers, not scientists.