What "could" a soul be? Well, the mind-uploaders might have an answer for that question someday. Perhaps it's a strictly bio-electrical phenomenon. I still hold to my conclusion that life is not a chance occurrence but a statistical necessity in the Universe, so it's not as if a soul must be mystical.
If you trust the standard definition of the soul, then the argument freezes there. We doubt everything else about Christianity, for instance ... why not doubt the definition of the soul? Without hostility, sarcasm, or otherwise--for it might be possible to interpret it that way--the result of trusting the Christian definition of the soul in order to argue about it seems more a tool to beat down an idea rather than to explore its possibilities.
Do you trust an ancient, possibly deluded people to define the terms of consideration you award a concept?
What bugs me is when an atheist who has rejected the Christian god that he or she learned in the world applies that to all Gods, even those they may never have heard of. This is the height of arrogance and contradiction, as it makes the atheist religious.
However, in this case, as I have pointed out above, you're letting people you don't trust set the considerations for the definitions.
In other words: Should someone someday find a "soul", do you really expect that it will look like people have described in religious philosophy?
But is there not a possibility that the limited linguistic scope of the past might stain the present considerations?
Is there any one idea of a soul? No. There are many diverse ideas of what the soul is. If we limit ourselves to the characteristics of any one idea, we limit our scope of inquiry. However, we are also limiting our scope of inquiry if we accept at face value what is said.