If you have witnessed (or taken part in) a debate between a religious person and an atheist the religious person will often make the assertion that atheism is a belief system as well, or that atheism is a 'faith'. The atheist will usually reject this notion and assert that atheism is merely a singular disbelief in God, not a belief system. The atheist is technically right; atheism in and of itself is not a worldview just as theism is not. However every atheist HAS a belief system or worldview or 'faith', of which atheism is one of the tenets of that worldview. For example there are nihilists and secular humanists. Both are worldviews that have atheism as a fundamental principle.
This being the case, while one can't rightly say that atheism is a belief system, one can say that atheists HAVE belief systems, and it can then be examined which of these belief systems is the most internally consistent, given atheism as the fundamental premise. That is, starting with the assumption that atheists (specifically naturalists) make which is 'the natural world is all that exists', we can determine which worldview best conforms with this assumption. And if an atheist's worldview is not consistent with the consequences of this assumption, the atheist will be forced to either reject his current worldview in favor of either a coherent atheistic worldview, or for a theistic worldview.
"You can not get an 'ought' from an 'is'"
David Hume expressed this notion that one can not derive an 'ought' from an 'is'. Essentially that you can not derive morality from facts and data. Since then some have tried to refute this argument (Searle), but unsuccessfully. You indeed can not derive an 'ought' from an 'is'. This is problematic for any naturalist who also claims to have a belief in morality. If the natural world is all that exists, then all that exists are 'is's. The naturalist claims that empirical observation of the natural world is the only method of determining truth. If this is the case, then a naturalist can not affirm any belief in morality (as anything other than arbitrary human delusion) without being inconsistent with his own beleifs. We know what the physical world IS and we have broken in down to it's most basic elements. If atomic particles and energy are all that there IS, then it is of course to absurd to state that atomic particles 'ought' to go left, or they 'ought' to go right. That electrical currents 'ought' to go up or 'ought' to go down. And humans, in the eyes of the naturalist, at our most basic level, are nothing other than atomic particles and electrical currents going up or down, left or right.
If the universe is a chain of undirected causal events, then 'oughts' can have no meaning. The nihilist recognizes this, and therefore rejects all notions of morality. While I disagree with the nihilist that the natural world is all that exists, if we grant him this premise, then his worldview is AT LEAST internally consistent. Just as if you grant the Christian the premise that Jesus Christ is God's only son, then pretty much all the rest of the Christian's beliefs will be internally consistent. The vast majority of atheists however are not nihilists, they are mostly affirmed secular humanists, secular humanists who don't self-describe at such but who hold the same beliefs, or some third worldview that is often very similar to secular humanism in the most relevant ways. And, unlike nihilism or Christianity, even if we grant the secular humanist his fundamental assumption (the natural world is all that exists), we find that this system of beliefs is NOT internally coherent or consistent. Because secular humanism also affirms the existence of things such as justice, morality, goodness, evil etc. Despite having no foundation from which to derive such concepts.
Therefore the naturalist must reject notions of justice, good, morality etc. as nothing more than human abstractions with no real use or purpose, if he is to be consistent, and adopt a nihilistic world view. Or reject metaphysical naturalism altogether. Now, the naturalist will likely respond that what we call morality is important biologically because it's based on self-preservation and survival. The problem with this argument is that it assumes that self-preservation, survival, propagation of the species etc. are inherently good, desirable goals. Which is a reasonable assumption, but not one that can be shown to be true through empirical observation, which they claim is the only way to know anything. Thus the naturalist who affirms belief in morality (as something other than arbitrary delusion), has a self-refuting world view.