I don't accept substance dualism or any belief/philosophy that indicates we have immaterial (nonmaterial) souls. One problem I have with appealing to the spirit world in order to buttress dualism in the human sphere is that we don't know how things operate in the spirit (non-material) realm; nor do we know how the spirit realm interacts with the physical world. So how can we try to support dualism by appealing to Jehovah interacting with our world or Jesus becoming a man, then becoming non-material again, if we don't know how any of these events happened (i.e., the exact mechanisms/processes that brought these effects about)? Worded another way, I attempt to explain obscure things by using more transparent and certain data; however, I'm not denying that Jehovah or the angels can interact with the physical realm. Some divine effects produced in our world are likely brought about directly (through remote causes) whereas others are produced indirectly (by secondary/proximate causes). Yet we don't understand how Jehovah directly interacts with physical things; we don't comprehend how Jesus became a man or how he became spirit again. That is to say, we don't fully understand the exact causal mechanisms/processes, which made these effects possible.
For the sake of argumentation, I concede that dualism is possible (logically or metaphysically), and that minds could possibly be immaterial. What I don't concede is the logical entailment: "If a non-material world exists (p), then an entirely physical world or human sphere cannot/does not exist (q)." Adding "possibly" to q (the consequent) doesn't seem to help much either. It's not clear how one statement logically entails the other. Additionally, as I maintain above, trying to explain material phenomena by evoking spiritual phenomena is highly problematic. It's like explaining temporal causation by means of atemporal causation, something we do not understand. Lastly, I think the term "dualism" needs to be clarified, although this concern is tangential.
Scientific work is just beginning (in earnest) on these kinds of problems. The neuroscientist Antonio Damasio has written books that attempt to integrate free will and a physicalist account of the self. He and Hanna Damasio (along with many others) have extensively studied the case of Phineas Gage, and given an account of what it potentially tells us about mentality. See Descartes' Error by Antonio Damasio. I also have a book that I've begun reading entitled The Neuroscience of Freedom and Creativity: Our Predictive Brain written by Joaquin M. Fuster (Cambridge Press). Joel B. Green has published works that partly address these issues as well. Admittedly though, much work needs to be done in this area. I would not agree that it's impossible in principle to explain memory (for instance) or pain in (Christian) physicalist terms, since pain can be explained by the overabundance of uric acid or the wearing away of cartilage (etc). Long-term memory can be accounted for by invoking the hippocampus or the fight/flight response can be explained by the amygdala. Physicalists have worked on qualia too, with no definitive result. Identifying qualia within a materialistic framework is still a lively and open question in the philosophy of mind. Almost every writer I've read accepts the existence of qualia, but there's no unanimous consent respecting how we experience "raw feels" or subjective sensations. Does dualism fully address this question? Not to my knowledge.
Yes, I agree that an explanation needs to account for how something works. That's one problem I have with dualism though. One first has got to substantiate the actual existence of the mental in the human realm before he/she proceeds to explain the mental. All I've seen demonstrated by any anthropological dualist is the logical possibility that we are two things: no one has ever conclusively proved that we have souls/spirits/non-material minds. Nor has the mind-body problem been solved by dualistic anthropology. As a matter of fact, it was a dualist who raised the difficulty of the mind and body problem (Descartes). We're still vigorously discussing this issue in the philosophy of mind and in neuroscientific circles. May I also demur a little and say that many physicalists take great pains to rationally justify their ideas and findings. I don't know if it's fair to say that Damasio, Joseph Ledoux, Francis Crick or Llinas have simply assumed that it's possible for neural processes to generate abstraction. The last author (Llinas) has written an entire work on the subject, and he's been interviewed and done extensive work on PBS here in the States. I can assure you that he's not merely assuming physicalism can possibly explain mind. We already know that there are neuronal correlates which can be mapped onto mental phenomena (e.g., depression and serotonin deficiency). It's just a question of proving that the correlation between the neuronal activity and the mental phenomena demonstrates causation, which is difficult to accomplish by using a posteriori means.
Both approaches have explanatory gaps. Dualism has not resolved the problem of free will or the mind-body problem. As I've sometimes pointed out to my classes: The mind-body problem is one that entails causal interaction (hammer hits thumb, I feel pain or beer goes down throat and I feel euphoric). How can something mental exert causal force on something that is physical? Granted, dualism allows for interaction between the mental and the physical, a dualist might appeal to the spiritual realm to support the idea that we're composed of two substances. Nevertheless, dualism still doesn't tell me how a physical event (hammer hits thumb) causes a mental event (I feel pain): the explanatory gap apparently remains. Or how is it possible for a non-material entity like the soul/spirit to move a 200 lb. object like a human being from point A to point B. I don't know of any dualist books/writers that offer satisfying or conclusive resolutions to these questions.