At Uncommon Descent William J. Murray lists ten reasons why atheists are "delusional." I'd prefer the word "inconsistent, or perhaps "irrational," but nevertheless, his ten points make for a compelling case that whichever descriptor one chooses, atheism is intellectually untenable and very difficult, if not impossible, to live out in consistent fashion.
Here are the first four of Murray's ten reasons in italics with my comments added:
1. They [atheistic materialists or naturalists] dismiss morality as nothing more than strongly felt subjective preference, but admit they act as if morality is objective in nature. They tacitly act as if morality is objective, for instance, every time they make a moral judgment of someone else's behavior.
2. They speak, act and hold others responsible for their behaviors as if we all have some metaphysical capacity to transcend and override the deterministic effects of our body’s physical state and causative processing (free will), yet they deny any such metaphysical capacity exists. In other words, if materialism is true there's scant grounds for believing in something like free will, yet every time someone uses the words "ought" or "should" in a moral sense they're implying that a person is free to have done other than what they did.
3. They deny truth can be determined subjectively while necessarily implying that their arguments and evidences are true and expecting others to subjectively determine that their arguments are true. If truth really is nothing more than a subjective preference then there's no point in an argument nor in stating any proposition with the expectation that anyone else should believe it.
4. They deny that what is intelligently designed can be reliably identified when virtually every moment of their waking existence requires precisely that capacity. Put differently, the extremely complex structures and information that must have existed in even the earliest cells they impute to chance but would never attribute to chance the ability to create the even more complex information contained in the operating systems on the computers they use every day.
Follow the link for the last six of Murray's reasons.
I said above that I prefer the word "irrational" because, as Murray points out with his ten reasons, naturalists can't live, or don't live, consistently with their fundamental assumption of atheism. To ignore the logic of one's fundamental assumption and to live as if its contrary were true, i.e. to live as if God exists while denying that he does, is a tacit admission that one's basic metaphysical assumptions are unlivable, if not incoherent. We might call this atheism's coherency problem.
Parenthetically, atheists of both a modern and postmodern predilection have an interesting relationship with reason. Modern man argues that reason is our most trustworthy guide to truth while the postmodern argues that reason is a failure as a guide to truth. Yet both must employ reason in order to make their respective cases. So, the modern has to assume reason is trustworthy in order to argue that it's trustworthy, which is surely question-begging, and the postmodern has to assume reason is trustworthy in order to argue that it's not trustworthy at all, which is surely self-refuting.
In neither case, can it be said that the modern or the postmodern is thinking rationally. We can have confidence that our reason generally leads us to truth, especially metaphysical truth, only on the assumption that God exists, is himself rational, and has created us in his image.
If we assume that God does not exist then we must conclude that our rational faculties are the product of processes which have produced those faculties to suit us for survival, not for the attainment of true beliefs, in which case there's no basis for thinking that they're trustworthy guides to truth. C.S. Lewis was one of the first to point this out as a trio of philosophers discuss in this video:
The same argument is an integral part of philosopher Alvin Plantinga's Evolutionary Argument Against Naturalism which he discusses in this video: