At the risk of retreating into sterile dictionary definitions, strictly speaking, atheism does not deny the possible existence of a supreme creative intelligence of the “unmoved mover” variety postulated by Anselm or even the “ground of being” beloved of modern sophisticated theologians like Tillich or Plantinga. What atheism denies is the existence of describable gods that actively intervene in the world, can be influenced by prayer or who actually give a shit about the human condition.
This is not to say that there aren’t good philosophical reasons to doubt the existence of the first concept, but it is one that most atheists are agnostic about to the extent that we either can’t know or at least don’t know yet whether such an entity is necessary . The second variety of god however is a different matter. Not only can we falsify all the claims made for such deities and so pretty much write them out of existence it actually matters that we do so and try to explain why.
Deistic concepts of god are abstract and philosophical: interesting mainly as potential explanations for why there is “something rather than nothing,” or “the unreasonable effectiveness of mathematics in science”. But, suspect as these explanations might be it does not matter on a daily basis whether they are correct or not as science will proceed to its conclusions whatever and nobody makes moral judgments or enacts legislation on the basis of this ontology.
According to their adherents theistic gods, existential or no, actually do things; they have opinions, dictate dress codes, define marriage, circumscribe sexuality, restrict diets, grant wishes, deny wishes, exact retribution, show mercy, send disasters, save us from disasters, require genital mutilation, demand worship, have sacred spaces, promise lands, sanction war and bless nations. Although which of these they do and for or to whom depends on which deity we are discussing. Yahweh has a thing about shellfish for example, Allah not so much.
Once you postulate a god that gets its hands dirty in the business of humanity a cabal of the righteous will soon be telling you exactly what that god requires of you and regardless of what your own sense of morality or personal thriving may say you had better listen and comply. Even if your god is of the more benign variety and its putative demands seem reasonable if not rational there is always the risk that someone with more power than you will decide it has taken a vindictive attitude towards something you cherish.
Luckily, we do not have to bend to the whims of these theistic tyrants or their apologists. Atheism, that’s a-theism, is justified by science, observation and rational inference to be the reasonable default assumption. Those “evidences” of such gods as are to be found in scripture are dispelled and proved to be false. Pace Rabbi Sacks, showing “that the first chapters of Genesis are not literally true, that the universe is more than 6,000 years old and there might be other explanations for rainbows than as a sign of God’s covenant after the flood” is an important first step in dismissing the reality of Allah, Yahweh and God in the same way that a lack of activity on Mount Olympus disposes of the Greek pantheon. Similarly the problem of evil is a strong philosophical counterpoint to the assertion that an omniscient omnibenevolent god has our best interests at heart and ridiculing prayer as an effective prophylactic against disaster is amply justified by its track record.
The existence of theistic gods is an absurd and easily refuted fiction which is why many religious apologists fall back on cosmological and ontological justifications that really only speak for the deistic gods of distant creation and divine apathy, but nobody cares about them. Christian theologians attempt to argue from ‘anthropic principle’ to ’ergo Jesus’ but there is no logical connection. You cannot get from an “unmoved mover” to any of the gods peddled by religion and a good thing too. A-theism allows us all to build our society on a strong secular ethic, free from moralising but not from morality, by accepting the undeniable truth that there are no gods to guide, beguile or coerce us into error.
"Religion is a hypothesis about the world: the hypothesis that things are the way they are, at least in part, because of supernatural entities or forces acting on the natural world. And there's no good reason to treat it any differently from any other hypothesis. Which includes pointing out its flaws and inconsistencies, asking its adherents to back it up with solid evidence, making jokes about it when it's just being silly, offering arguments and evidence for our own competing hypotheses...and trying to persuade people out of it if we think it's mistaken. It's persuasion. It's the marketplace of ideas. Why should religion get a free ride"