The ‘traditional’ objections to a wholly naturalistic metaphysics, within the modern Western philosophical tradition, involve the vexed notions of freedom and consciousness. But there is, I think, a much deeper and more interesting line of criticism to naturalism, and that involves the notion of intentionality and its closely correlated notion of normativity.
What is involved in my belief that I’m drinking a beer as I type this? Well, my belief is about something — namely, the beer that I’m drinking. But what does this “aboutness” consist of? It requires, among other things, a commitment that I have undertaken — that I am prepared to respond to the appropriate sorts of challenges and criticisms of my belief. I’m willing to play the game of giving and asking for reasons, and my willingness to be so treated is central to how others regard me as their epistemic peer. But there doesn’t seem to be any way that the reason-giving game can be explained entirely in terms of the neurophysiological story of what’s going on inside my cranium. That neurophysiological story is a story of is the case, and the reason-giving story is essentially a normative story — of what ought to be the case.
And if Hume is right — as he certainly seems to be! — in saying that one cannot derive an ought-statement from an is-statement,and if naturalism is an entirely descriptive/explanatory story that has no room for norms, then in light of the central role that norms play in human life (including their role in belief, desire, perception, and action), it is reasonable to conclude that naturalism cannot be right.
(Of course, it does not follow from this that any version of theism or ‘supernaturalism’ must be right, either.)