Specifically, the criticism seems to be that calling oneself an atheist commits you to the position that the material world is all there is, to the exclusion of any and all supernatural or dualistic possibilities. There is so much about the world that remains unexplained, and so much we likely haven't even discovered that will need explaining, that it's absurd to assert that there's nothing more to reality than material "stuff". Right?
That door would seem to swing both ways: you might say, "You can't prove that there won't be a material explanation for anything and everything!" Both assertions are trivial, because we're fully aware that there's a lot of stuff we don't understand or could potentially discover, and it's entirely possible that some supernatural explanation could enter the picture at some point.
BUT... We have pretty damn good reasons to think that supernatural explanations aren't relevant.
The first is a conceptual problem. Take, for example, the dualist theory of the mind. Supposedly, the mind exists independently of the brain and interacts with it somehow. This is usually rooted in an argument from ignorance – the dualist will describe some "mystery" of consciousness, like subjectivity or intentionality, implying that a dualist hypothesis can explain this mystery while materialism cannot. But in order for it to be a non-trivial explanation, the dualist has to define what the non-physical mind actually is, how it exists, and how it interacts with the physical brain. Until these things can be done, dualism can't actually be tested – and if it can't be tested, there's no way to know for sure whether it's right or wrong.
Meanwhile, the materialist explanation of the brain has worked profoundly well. In the book The Science of Evil, Simon Baron-Cohen details the empathy pathways in the brain and how they affect our ability to experience and conceptualize empathy in highly specific ways. Damage one part of the brain, and you can't feel empathy at all; damage a different part, and you can feel empathy but it won't be triggered by facial expressions; damage another part, and you can feel empathy but be clueless as to how to act on it (the natural response is physical mimicry, like when we assume a slouched posture while comforting a grieving friend).
Examples like this abound. You can lose the ability to recognize faces, or preserve that but lose the ability to remember names. Your sexual orientation can change, and you can even lose the ability to conceptualize the left or right side of anything (it's called hemispatial neglect). All of this clearly points to a causal relationship between the brain and the mind. A dualist will inevitably try to dismiss it all as correlation, but there's a problem: there are exceptions to correlations. For example, let's say there's a correlation between eating fast food three times a week and being obese. It doesn't follow that everyone who eats fast food three times a week will be obese, because there are lots of other causal factors at work.
But in the case of the brain, it's always the case that damages will produce specific responses depending on the area of the brain damaged. It's not as though you can damage one part of the prefrontal cortex and be fine, while another person equally damages the same part and suffers severe disability. We can use our growing understanding of the brain to predict states of subjective awareness, sensations, emotions, and thoughts. That's pretty powerful evidence of a material aspect of the brain. To paraphrase Stephen Hawking: science wins because it works.
There's a bigger issue though, which is that there's nothing in science or materialism that in principle rules out supernatural explanations. To expand on the example a few paragraphs up, the dualist has to answer questions like this:
- How does the mind exist without the brain?
- What is the mind made of?
- If the mind exists independently of the physical universe, what laws govern its properties and behaviors?
- What is the mechanism by which the mind interacts with the brain?
- How could a dualist theory be tested? What predictions can it make?
In other words, such things would simply be part of our growing understanding of reality. But as long as these concepts are defined in such a way as to permanently keep them beyond the purview of investigation, then they're just positing an idea that is irrelevant. It might be true, but with no means to verify it, it might as well not be true. And that's precisely the position that those who object to materialism find themselves in. They recognize the overwhelming success of material explanations, but they still feel a need to cling to supernatural things – generally because it's hard to reconcile their theology without it. But they then define the supernatural in such a way that we can never really know whether it exists or not. It can never be tested or add any non-trivial information to our understanding of reality. In that case, even if the supernatural does exist, we'll never be able to know – in which case it might as well not exist.