And for that reason, we'll never discover the soul. It will perpetually be that "something" that we are missing in our understanding of things. Assume for a minute that we have the basic picture correct, that there is no non-physical soul: your belief would have us searching for the rest of time! Isn't it best to suspend the question?
There probably isn't any simple causative explanation (as in the example you provide). The brain is the most complex structure we know of and "self" arises from that deep complexity; this is an answer that I'm content with, as anything more in-depth / closer to the "metal" would quickly exceed my ability to understand it.
> we'll never discover the soul
What if it reveals itself to us?
Maybe - let's assume that we could simulate a human brain to a high level of fidelity starting from a known good state and emulate its input and output. Do you think we could poke at it enough and ask the simulated person about their experience enough to discover the mechanisms behind what we experience as a soul? It's logistically and computationally insanely complex to pull off, but if we could build such a system, I don't see why we couldn't eventually figure it out in another thousand years' time (assuming we don't destroy ourselves or do something that sets back the evolution of technology massively between now and then).