Professor Hall argues that "today’s atheism tends to stand on an absolutely self-contradictory claim: only that which can be seen can be known. (It’s a pseudo-scientific claim.)". Generalizations are, by definition, not confined to asserting only that which has already been directly observed. Professor Hall points out that atheism is itself a generalization (it is not a directly seen object). So by rejecting generalization atheism is self-contradictory. Is Professor Hall right? Is this a fatal flaw with a central premise of atheism?
Atheism is rooted in dismissing as probably false those factual conclusions that lack a logical connection to something that has been observed, particularly when our observations are instead logically connected to a contradictory factual conclusion. There is a subtle but critical difference here with Professor Hall's straw-man mischaracterization of atheism's underlying premise. Atheism affirms that we can indirectly infer from logical connection with observations while Professor Hall is mistakenly claiming that atheism denies this possibility. Atheism is a best fit logical inference from our observations regarding how the universe functions (this is one of the reasons that I refer to my atheism as a belief). Thus there is nothing here that is "self-contradictory" or "pseudo-scientific". Scientific theories are similarly logical best fit with observations models and as such are also generalizations rooted in observations.
Metaphysical naturalism is a very broad generalization and there is no correspondingly broad consensus that metaphysical naturalism is true, therefore atheism is not a science textbook conclusion. Yet atheists are employing an iterative inductive/deductive, empirical based, approach to try to distinguish fiction from fact. This is the same approach utilized by good plumbers, engineers, medical professionals, historians, philosophers, etc. This is the approach taken by infants when they opt to avoid walking over transparent floors that are suspended high above the ground as they develop an awareness of the risk of falling from experience (it takes more time to learn that the transparent floors are nevertheless safe). We know that science is successful only when it employs naturalistic methods and reaches naturalistic conclusions. Therefore it is metaphysical supernaturalism, not metaphysical naturalism, that is the more self-contradictory and psuedo-scientific (and also presumptuous) belief.
It is no surprise that theistic academic theologians working at religious institutions, such as Professor Hall, prefer an "old time atheism" that is focused on existential angst because then they can promote theism as a form of therapy. Theists often elevate psychological and purely intellectual considerations over empirical considerations (and agnostics often prioritize what we do not know over acknowledging what the available empirical evidence communicates). If this is the best that academic theologians can do in arguing that atheism is unjustified, and I believe that this is close to the best they can do, then they have little prospect of winning this argument.