Ok, I'll jump in.
I think we will have to speak of being souls, rather than "having" souls. The latter gives the impression that we are beings that are not souls, but rather have souls. Those entities are presumably not bodies either, because if they were we would be equating ourselves with our bodies and then positing a non-physical soul that we happen to have. But no one wants to do that. There are a few Christians who do want to say that we are wholly material beings (I'm not one of them), but the whole point of that is to avoid having to posit anything non-physical that we are or have. So it makes much more sense to say that the view we're considering here is that we humans are non-physical souls that have bodies closely associated with them.
Some Christians like to distinguish between mind and spirit and soul (and the body is yet a 4th thing). Maybe there is a distinction to be made here, but let's not get into that. Whatever trouble might be forthcoming as a result of evolutionary biology, it will concern the existence of any non-physical thing. If there is trouble for one such non-physical thing there will be trouble for two or three of them, and likewise if there is no trouble. So let's just talk about one non-physical thing, call it a "soul," and then say it is the entity that can be aware of things, have beliefs and desires and affections, can reason and deliberate, can experience sensations, have memories, etc. That way "mind" and "spirit" become aspects of the "soul," but are not distinct entities. And a soul does seem to be what we take ourselves to be.
I do not understand how anyone can claim that we have no reason to think that we are souls. The mere fact that the majority of human beings have thought so should give us some reason. But perhaps they mean only that we cannot empirically verify that we are souls, or that what people have thought for centuries has been obviously defeated by recent empirical investigation. So we need an argument to think there are souls that is not obviously defeated by recent empirical investigation. Ok, here's one (and it's not new):
The fundamental constituents of matter lack the capacity for consciousness. (Actually, they lack all the capacities ascribed above to souls, but for simplicity's sake we may limit ourselves to talking about "consciousness." But the list obviously includes more than just the capacity to "be aware.")
Anything that is composed exclusively of things that lack the capacity for consciousness, likewise lacks the capacity for consciousness.
All "physical things" are composed exclusively of the fundamental constituents of matter. (This includes our bodies, and all parts of our bodies, which in turn includes our brains.) This is merely a reasonable definition of "physical thing."
Therefore, 4. All physical things lack the capacity for consciousness. (This follows from 1, 2 and 3.)
Five (5). Humans have the capacity for consciousness.
Therefore, 6. Humans are non-physical things (i.e., souls). (This follows from 4 and 5.)
I do not take this argument to prove to all reasonable people that humans are souls. Recall that this is a response to the claim that we have no reason to think there are souls. So it is intended only to supply a good reason, even today, to think there are souls. I am not claiming that the argument cannot be defeated by further inquiry. I am saying only that the argument is reasonable on its face, i.e., it is prima facie reasonable. However, to defeat it, one must deny either 1 or 2. [3 is clearly a reasonable definition, and 5 is an undeniable fact of experience. And the argument is clearly valid. So anyone who remains unpersuaded must think that either 1 or 2 (or both) is false.] The bulk of the scrutiny will center on 2, but some people are pan-psychists who will deny 1. Regardless, it should be clear that we all have some reason to think there are souls. That's because 2 seems very hard to deny. How can anything conscious ever be composed exclusively of non-conscious things? Some properties can indeed "emerge" when parts that don't have the property compose a whole that does have it (sphericity, for example). But consciousness does not look like one of those potentially "emergent" properties at all. The burden of proof is on those who say that consciousness can thus "emerge." And this is the problem that psychologists and philosophers of mind have called "the hard problem of consciousness." It has not yet been solved. The burden of proof has not yet been met. Piling up correlations (as neuro-scientists have certainly done much of lately) between physical and mental events is not sufficient to solve the problem. We can still ask what the relationship is between mental events and their physical correlates, without equating the mental with the physical. (The Cartesian intuition cannot be glibly cast aside merely on the basis of correlations.) So we have some reason to think there are souls. There is no more room for saying we have no such reason.
Finally, I wouldn't mind it at all if someone could show that something non-physical could "emerge" from a suitably sophisticated arrangement of matter. That would solve the problem very neatly, and it would allow for the possibility of this non-physical thing to survive the dissolution of the matter from which it emerged. And it would solve the problem not only in the evolutionary case of souls emerging in animals whose ancestors were not souls, but also in the parallel case of physical embryos that somehow "generate" souls at some (hard-to-define) point in their development. The evolutionary problem seems to me to be the same as the embryonic problem. If we can solve one, we'll solve the other.
I don't have a solution though. Sorry. (But I still think #2 above is true.)