The problem is how an entity which is apparently immaterial like the human consciousness – it exists, but you can’t locate it, much less measure it – can have arisen from something purely physical, like the arrangement of cells that make up the human body.
You can say the same for abstract concepts like efficiency, health, power, racism, immensity, height, etc. Can you physically locate efficiency? If not, does that mean that efficiency has a soul, or that it's some overly complicated conundrum? Not really.
And yes, you can measure consciousness. Energy is a great analogy for consciousness, because it's not a physical substance in itself; rather, it's a measurement of the ability of physical objects to perform work. You can't feel, taste, touch, hear, or smell energy, but you can know that it exists, because it, by definition, is nothing more complicated than a capacity. Consciousness is just a measurement of the work done by neurons -- a process; in other words, even if it is not the sum of the neurons themselves, it can be demonstrated to be a property or by-product of the neurons for the same reasons that a tornado or river (or their energy content) can be demonstrated to be properties of physical matter, but are not themselves limited by it.
Just because a process is not limited to an unchanging set of physical matter doesn't mean that it requires magic in order to be explained, or that it is somehow beautifully complex; conceding that this is true for just about any abstraction, process, or measurement while simultaneously allowing consciousness to be an exception is preferential thinking at its worst.
The crux of the article, though, has to do with why people mistakenly believe that they have a soul, which is fine, but the issue is made out to be needlessly complicated:
No one has produced any plausible explanation of how the experience of the redness of red could arise from the actions of the brain. It appears fruitless to approach this problem head-on.
I can't make sense of this at all. Anything that confers an evolutionary advantage, no matter how intuitively incomprehensible it may be to us, will be selected for, because the universe will use any impetus or motivator that it can to keep life going. Analogously, the two options with which we're currently presented as explanations for the universe's existence -- that there was a point in time before which no causes existed, and that causality is infinite -- make no sense to humans intuitively, but that doesn't imply that there absolutely must be a third option.
Your brain's inability to imagine things which it did not evolve to imagine does not in any way demonstrate that those things are not business as usual for reality.
As for the subjective feeling of "being" a soul, or an ego that "pilots" a body, I fail to find this phenomenon any more exceptional than any other evolutionary motivator, including non-sensitive reflexes, or even genetic instructions to consume chemicals. When you say things like, "It's truly a marvel how the brain has devised a mechanism for encouraging the reproductive success of organisms by way of thoughts, feelings, awe, wonder, and a sense of beauty," it just sounds like, "I'm in awe of the fact that living things have the capacity to be in awe," or even, "It's amazing how living things are controlled by genetic instructions for no reason whatsoever" to me.
For future reference, here are some immaterial entities which probably exist, but which also probably do not have souls:
You know what? This list could contain thousands of items, so I'll stop here. Consciousness is not special.
Update: Maybe the following idea will be of help to those who think that consciousness is special simply because it is slightly more complex than its surroundings:
Consciousness, like rivers or exercise, doesn't merely "exist" -- it happens. Think of anything that happens, and you'll soon realize just how unspecial consciousness really is. Can you quantify a baseball game? Can you hold it in your hands? Can you pinpoint exactly where the game is and label it as a material object? No, but baseball games happen, which is something else that the universe allows for. Consciousness happens; our brains are the stadiums.