One of the great advantages of the naturalist world view is how it all hangs together. The workings of the mind can be explained in terms of the workings of the brain, which can be explained in terms of the workings of the brain cells, which can be explained in terms of the electrical and chemical properties of molecules, which can be explained in terms of the physical properties of the particles of which those molecules are composed. And the same goes for anything else in the universe: stars, moons, clovers....
Now, I will admit that some of the links in that proposed chain of explanation are not as strong as others: the mind-brain link, for example. But the overall scheme seems sound, and the naturalistic world view can count innumerable successes as evidence of its truth: the technologies of transportation, agriculture, communication, medicine, and psychiatry, to mention just a few. Put this against the abject failure of alternative ways of thinking: what did Christianity (just to pick on one alternative) accomplish in the 1500 years before scientific thinking arose?
At any rate, even when precise explanations are lacking, there doesn't seem to be any strong argument why the gaps cannot be filled out in a naturalistic way.
It seems, though, that many atheist philosophers are no longer satisfied with this reductionistic picture. The recent book Mind and Cosmos, by atheist philosopher Thomas Nagel, argues that there are aspects of subjective experience that can't be explained by reductionistic means. (Short version here.) Another atheist philosopher, Philip Kitcher, whom I have the greatest respect for, disagrees with Nagel but seems to agree that the reductionist program has not accomplished the task it set out to do. "Unity fails at both ends," writes Kitcher.
For once, I agree with Professor Feser: if naturalism fails to give us a unified picture of everything, then it is time to abandon naturalism and seek a different explanation, rather than to cling to a failed program.
But I am not as pessimistic as these philosophers. Perhaps that's merely ignorance on my part. But some of the anti-reductionist arguments I've come across seem just silly, and, as I already said, there don't seem to be any good arguments for the impossibility of naturalistic explanation. I remain a hard-core reductionist, and I'm going to try to defend that view.
Next: Do the laws of physics lie?