One of the great insights of modern neuroscience is the way that our phenomenological experience can be profoundly and counter-intuitively altered when various regions of the brain do not function properly. You can lose the ability to feel empathy; or, you can retain the ability to feel empathy but lose the intuition for reciprocation (i.e., empathetic behaviors). You can lose the ability to recognize faces, or forget the names of people but remember the names of tools. Your personality can be dramatically altered by variations in your neural composition.
The reason this is counter-intuitive is because we tend to view our personalities, and those of others, as fixed. I am who I am, and that's just the way it is. Joe is the way Joe is, Jane is the way Jane is. If Joe suffers from pathological narcissism or Down's Syndrome, that's just the way Joe is. If Jane is exceptionally compassionate and selfless, that's just the way Jane is.
People do recognize that life experience plays a crucial role in shaping our personalities, but we tend to underestimate just how much our biology factors into the picture. Humans are no different from animals in that our temperament is powerfully influenced by our biology, as are our moods, emotions, and our ability to think critically.
So what if consciousness is not what the brain does, as a non-eliminative physicalist like yours truly would view it, but rather consciousness is ultimately disembodied and merely runs on the brain like software — and, in our bodily death, our consciousness will somehow rise off the brain and we will experience some sort of new, non-physical reality?
A substance dualist would take the view that when the personality of an individual is irreparably altered by trauma to the brain, the 'true' personality of the person still exists — it simply is not being fully realized because the brain is not functioning properly. But this raises an interesting conundrum for a blissful spiritual afterlife (which, as I've argued many times, is already littered with logical and conceptual problems , , , ): who would we actually be in Heaven? Would we recognize ourselves, or others?
If, for example, we take Joe the pathological narcissist, he might be kind of asshole through little fault of his own. He is literally unable to feel empathy the way the rest of us do; his moral and social behaviors are based purely on utilitarian considerations. And, as humans, we tend to see this as fixed. So, will Joe be cured of his narcissism in Heaven (assuming narcissists can attain salvation), since his consciousness is now untethered from his abnormally-functioning brain? If Joe has Down's Syndrome instead, will he no longer be recognizable as the disabled individual he spent his whole life being?
I suspect many believers would want to answer in the affirmative, but doing so only complicates the issue. What about Jane, who is ultra-compassionate? Jane, like a rare few, has an exceptionally high level of empathy. Her brain functions abnormally, but it makes her an exceptionally loving, selfless person — a model Christian, one might say. When her consciousness is untethered, does her personality revert to somewhere in what we would consider the 'normal' spectrum of brain function?
Consider also those who, through accidental brain trauma, have achieve some extraordinary new skill — like Jason Padgett, who gained the ability to perceive the world as complex equations and draw those equations by hand in exquisitely detailed form. Will he lose such an ability in Heaven, or will the rest of us gain it? Will musical savants become normal, or will we all become musical savants?
The problem dualism faces here is that when the consciousness is no longer tied to the brain, it's impossible to predict what the consciousness will actually be. Components of our personality that we take to be fixed and central to our personal and social identities, no longer being dictated by the composition of the brain, could change drastically or be gone altogether. Dualists don't know; they can only conjecture.
In what sense, then, is your disembodied consciousness really "you" at all? Not only could your personality and the personalities of those around you be altered such that they bear little resemblance to their embodied form, but even your language and your process of reasoning — which are shaped powerfully by your embodiment — will be necessarily altered such that they bear little resemblance to the version of you that exists here on Earth.
In my experience, believers tend to view the afterlife as essentially a continuation of their Earthly experience, perhaps enhanced in some way but fundamentally preserving their memories and personalities. But the fact of our embodied mind and the way in which our neurology is so centrally tied to our behavior show that if you were indeed a disembodied consciousness, you would bear so little resemblance to your Earthly self that it's not coherent to even call the afterlife a continuation of your embodied phenomenological experience. It seems that even if you believe you have an immortal soul, your Earthly personality would still be left behind with your corpse.