It has been said that without theism atheism wouldn't exist. In the philosophical sense this is true. A position in opposition to another can only be maintained as long as the other position exists. You can't be a non-gluber if there are no glurbers. You can't reasonably disavow that which no one avows. It's also true that without the word "theist" the word "atheist" would have no meaning.
But what does "atheist" mean? There are many opinions on that. Some sources say (for example) that it means "without belief or lacking belief" while others (for example) say that it means "the belief that there is no god or the denial that god exists". There seems to be some confusion as to what an atheist is. Is he a doubter in gods or one who insists gods don't exist? How is an atheist different from an antitheist or an agnostic?
As is it the case with theism, the best way to avoid confusion is to ask a person what they mean when they call themselves a theist or atheist. There is no single definition of Christian, Muslim or Jew. Within each of those general categories are many separations and divisions. If someone tells you they're a Christian does that mean they're a Baptist, a Catholic or a Unitarian? Is a Muslim a Sunni or Shia? Are they fundamentalists or liberal believers in their religion? You just can't tell without asking them to be more specific. It's the same for atheists. Some are what we call "hard" atheists. They say that without a doubt gods do not exist. Some are "soft" atheists who say that since no evidence exists establishing unquestionably that a god or gods exist it is most likely they don't. Again, the only way to know what a person means when they call themselves an atheist is to ask.
Hard atheism is a dogmatic stance with no more evidence to substantiate it than theism. To maintain adamantly that gods do or do not exist is to make a claim that can only be supported by the possession of absolute knowledge. Since we have no reason to believe that any human possesses absolute knowledge, absolute claims of the existence or non-existence of gods, or much of anything else, are irrational and can be ignored as baseless.
If theism is the belief in gods then "a"theism is the absence of belief. The prefix "a" means no or without. A person can be moral or amoral. An amoral person is neither moral nor immoral, they either lack or show an indifference to morality and immorality. An agnostic is someone who claims to have no knowledge (gnosis) of gods. They would have no opinion on the topic as they lack the knowledge to form one.(1) So my interpretation of atheism, based on word construction, the meaning of the prefix and my own personal attitude toward theism, is that an atheist lacks faith in gods. They have no belief. For me atheism implies no stance on the possible existence of undefined beings who may appear to us to be gods; it's the lack of belief in the gods man has worshiped over the centuries, gods well defined by their followers and with established attributes. Once a particular god is defined by its believers then there's a specific concept in which to believe or not believe. I am atheistic toward the gods of humanity, not the abstract concept of gods or god-like entities. The possible existence of that sort of thing, for now, remains unknown as we lack evidence for such things.
So atheism as I understand it and live it is a neutral position. It's a position that requires both those who insist gods exist and those who insist they don't to offer evidence to support their claims. It's not an absolute position but simply one awaiting substantiation of absolute claims.
(1) When T.H. Huxley coined the term "agnostic" he meant it to be both a philosophical position and a method for discerning truth. He quotes Kant, "The greatest and perhaps the sole use of all philosophy of pure reason is, after all, merely negative, since it serves not as an organon for the enlargement [of knowledge], but as a discipline for its delimitation; and, instead of discovering truth, has only the modest merit of preventing error." In Huxley's treatise on agnosticism he says, "When I reached intellectual maturity and began to ask myself whether I was an atheist, a theist, or a pantheist; a materialist or an idealist; Christian or a freethinker; I found that the more I learned and reflected, the less ready was the answer; until, at last, I came to the conclusion that I had neither art nor part with any of these denominations, except the last. The one thing in which most of these good people were agreed was the one thing in which I differed from them. They were quite sure they had attained a certain "gnosis,"–had, more or less successfully, solved the problem of existence; while I was quite sure I had not, and had a pretty strong conviction that the problem was insoluble. And, with Hume and Kant on my side, I could not think myself presumptuous in holding fast by that opinion."
It is with this in mind that I describe my postion on concept of theism as being an agnostic atheist. I am agnostic when it comes to the possibility that a god or god-like entity may exist somewhere, somehow, but atheistic toward the gods that mankind has worshiped throughout history, about whom much has been claimed without substantiation.
(A decent Wikipedia article on the various religious philosophies.)