Any individual trait I can actually grasp and specify, could be changed by altering the brain, so the idea of a unique soul allocated just for "me" has no basis in anything I perceive. How is my soul different from your soul when they're not occupying different bodies? And if they're no different from each other, why assume a multitude of them? Your first reaction may be to make an analogy with something material: every hydrogen atom is "the same" as every other, and there's plenty of those around; but that doesn't really work: different atoms can have different velocities, they can never occupy the same space etc., so even though they all have the same essence, they are not really the same. Leaving the world of matter, you have no such individualizing properties; two things of the same essence, are really just one thing. There are no souls as such.
On the other hand, consciousness is inexplicable in physical reductionist terms: if you were a hyper-sophisticated logical deduction system, with no fisrt-hand experience of subjective perceptions, you could never deduce them from examining the physical structure of a human brain; maybe you could deduce some kind of psychological model of motive forces that drive behavior, but none of that would be any more "real" to you than tensors -- you'd be playing around with abstract mathematical concepts conceived purely as tools to deal with complexity; you would never know what anything looks like, sounds like, feels like; you would never even know that something could feel like anything; you could never conceive of the experience of simply being, let alone explain it in terms of matter. None of this is to claim that consciousness is supernatural: so-called "physicalist" bigots simply have a habit of conflating "natural"/"real" with "reducible to atoms", when they could simply admit that consciousness, in its pure form, is another fundamental phenomenon of nature, rather than something tied to the atoms of a particular body.
