This would be unexpected if materialism were true, and in fact one neurosurgeon, Dr. Theodore Schwartz at Cornell, remarks that the fact that split-brain patients continue to think of themselves as a single self must be an illusion of some sort:
As a brain surgeon...I’ve severed the brain in two and watched in amazement as my patients wake up feeling like their complete and undivided selves. When I first did this type of operation, I had fantasies that they might suddenly refer to themselves as ‘we’ rather than ‘I’. Thankfully, this never occurred...the patient’s sense of a unified self is the illusion.Schwartz assumes that the patient's sense of being a unified self is an illusion because his materialism doesn't permit any other explanation, but another neurosurgeon, Michael Egnor, argues that there is indeed another explanation. Egnor asserts that "The split-brain patient’s sense of a unified self is real, not an illusion."
He adds that,
I say this for two reasons.Egnor develops his argument more fully at the link, but why does it matter whether a split-brain patient is one self or two?
1. It makes no sense to say that two people have an illusion that they are one person. To have an illusion presupposes that the subject with the illusion is one person. Two people would have two illusions, or they would have similar illusions, or share illusions, or conspire to claim to have the same illusion, etc. But having an illusion — even an illusion that I am one person after having my brain split in two — presupposes that I am a single person that has the illusion.
The claim that two people have one illusion...makes no sense.
2.There is clear neuroscientific evidence for unified consciousness in patients with split-brains. Neuroscientist Justine Sergent studied split-brain patients and found that while some perceptual abilities are indeed split — for example, the right side of the visual field is seen via the left hemisphere, and vice versa — there remains a genuine unity to the human mind.
Sergent showed images of different objects to each of the two split hemispheres, and found that patients could compare the objects reasonably accurately, even though no part of the brain perceived both objects.
If, despite the brain being split, we still perceive ourselves as being one person, then that's good evidence that there's more to us than just the matter that makes up our brains. It's evidence, in other words, that there's something essential about us that's immaterial - a mind or soul.
If this is true, materialism - the belief that everything in the universe is reducible to matter and energy - is false, but materialism is a major pillar of naturalism. If materialism is false then naturalism - the belief that the natural world is all there is - would be on the brink of collapse.
If materialism is false, if immaterial minds or souls do exist, then the belief that there is a Supermind that created the universe and all of life becomes even more plausible than it already is.