Atheist Austin Cline offers a brief but good overview of why atheists do not believe in gods, here.
Multiple Gods and Religious Traditions:
It is difficult to credit any one religion as being True or any one god as being True when there have been so many throughout human history. None appears to have any greater claim to being more credible or reliable than any other. Why Christianity and not Judaism? Why Islam and not Hinduism? Why monotheism and not polytheism? Every position has had its defenders, all as ardent as those in other traditions. They can't all be right, but they can all be wrong.
Contradictory Characteristics in Gods:
Theists often claim that their gods are perfect beings; they describe gods, however, in contradictory and incoherent ways. Numerous characteristics are attributed to their gods, some of which are impossible and some combinations of which are impossible. As described, it's unlikely or impossible for these gods to exist. This doesn't mean that no god could possibly exist, just that the ones theists claim to believe in don't.
Religion in Self-Contradictory:
No religion is perfectly consistent when it comes to doctrines, ideas, and history. Every ideology, philosophy, and cultural tradition has inconsistencies and contradictions, so this shouldn't be surprising — but other ideologies and traditions aren't alleged to be divinely created or divinely sanctioned systems for following the wishes of a god. The state of religion in the world today is more consistent with the premise that they are man-made institutions.
Gods Are Too Similar to Believers:
A few cultures, like ancient Greece, have postulated gods which appear to be as natural as human beings, but in general gods are supernatural. This means that they are fundamentally different from human beings or anything on earth. Despite this, however, theists consistently describe their gods in ways that make the supernatural appear almost mundane. Gods share so many characteristics with humans that it has been argued that gods were made in the image of man.
Gods Just Don't Matter:
Theism means believing in the existence of at least one god, not that one necessarily cares much about any gods. In practice, though, theists typically place a great deal of importance on their god and insist that it and what it wants are the most important things a person can be concerned with. Depending upon the nature of a god, however, this isn't necessarily true. It's not obvious that the existence or desires of gods should matter to us.
Gods and Believers Behave Immorally:
In most religions, gods are supposed to be the source of all morality. For most believers, their religion represents an institution for promoting perfect morality. In reality, though, religions are responsible for widespread immorality and gods have characteristics or histories which make them worse than the most vile human serial killer. No one would tolerate such behavior on the part of a person, but when with a god it all becomes laudable — even an example to follow.
Evil in the World:
Closely associated with taking action that should be considered immoral is the fact that there is so much evil in the world today. If there are any gods, why don't they act to eliminate it? The absence of substantive action against evil would be consistent with the existence of evil or at least indifferent gods, which is not impossible, but few people believe in such gods. Most claim that their gods are loving and powerful; the suffering on Earth makes their existence implausible.
Faith is Unreliable:
A common characteristic of both theism and religion is their reliance on faith: belief in the existence of god and in the truth of religious doctrines is neither founded upon nor defended by logic, reason, evidence, or science. Instead, people are supposed to have faith — a position they wouldn’t consciously adopt with just about any other issue. Faith, though, is an unreliable guide to reality or means for acquiring knowledge.
Life is Material, not Supernatural:
Most religions say that life is much more than the flesh and matter we see around us. In addition, there is supposed to be some sort of spiritual or supernatural realm behind it all and that our "true selves" is spiritual, not material. All evidence, though, points to life being a purely natural phenomenon. All evidence indicates that who we really are — our selves — is material and dependent upon the workings of the brain. If this is so, religious and theistic doctrines are wrong.
There is No Good Reason to Bother Believing:
Perhaps the most important and common reason for not believing in any gods and for not following any religions is the absence of any good reason for doing so. All of the above are decent reasons for not believing and are common reasons for questioning — and eventually leaving — whatever theistic and religious beliefs a person might have had in the past.
Once a person gets beyond the bias in favor of belief, though, they can realize something critical: the burden of support lies with those claiming that belief is rational and/or necessary. Believers fail to meet this burden, however, and as a consequence fail to provide any really good reasons to accept their claims. As a consequence, those who don't already believe and/or who are not biased in favor of belief aren't given a reason to start.
Given the fact that the burden of support lies first and foremost with those making the positive the claim — the theistic, religious believers — then non-believers don't necessarily need reasons not to believe. They are helpful, to be sure, but they aren't particularly necessary. Instead, what is required are reasons to believe.
The question "Why don't you believe?" is a request for justification from the nonbeliever; the response "I haven't seen any good reason to bother believing" returns the need for justification back to the believer where it belongs. Too often, believers fail to realize that their position is the one which needs defending and perhaps this can help them begin to understand that.
Of course, I add The Religion That a Person Adopts is Determined Almost Entirely by the Faith He or She is Exposed To, that's why I have proposed The Outsider Test for faith...