Absence Of Evidence Is, Indeed, Evidence For God's Absence
Jerry Coyne posts at Why Evolution Is True on the notion that you "can't prove a negative":
The "you can't prove a negative" argument is wrong. You can prove a negative, which means disproving a positive (i.e., God exists)--if you construe the word "disprove" as meaning "showing that the existence of a phenomenon is so unlikely that one would have to be blinkered or perverse to still believe it." And that is the case for God.
Scientists, of course, don't use the word "prove". We have greater or lesser degrees of confidence in phenomena. And when a phenomenon is supported by so much evidence that you'd have to be perverse to deny it (as Steve Gould put it), then we regard it as a fact, or "proven" in everyday jargon. I am immensely confident that the earth rotates on its axis, that a water molecule has two hydrogen carbon atoms, and that we evolved from other creatures very different from modern humans. I regard those claims as "proven" in any meaningful sense, but to preserve the provisional nature of scientific truth, I avoid the word "proof" in both technical and popular presentations.
...In the case of God, then, the absence of evidence is indeed evidence for His absence. We can provisionally but confidently say that there's no evidence for a God. and therefore reject the notion that He exists. (This could be revised, of course, and in earlier posts I've given some possible evidence that would convince me of divine beings.)
How the disproving thing works:
Can you disprove that I don't have a heart? Of course you can: just do a CAT scan! Can you disprove that I am not married? For all practical purposes, yes: just try to find the records, ask people, or observe me. You won't find any evidence. Can you disprove the notion that fairies live in my garden? Well, not absolutely, but if you never see one, and they have no effects, then you can provisionally conclude that they don't exist.
God is like those fairies.
He posts a few examples of the lack of evidence for god:
There is no evidence of divinity or miracles in the present world, and no palpable evidence of God-inspired miracles (prayers don't heal amputees).
God, despite being omnipotent and desirous of our knowing him, has never appeared despite his manifest ability to do so. He could, for example, write "I am Yahweh; obey me" in the stars. This is the "hidden God", the Deus absconditus. As philosopher Herman Philipse has noted, God should want each individual to know of his existence to create a reciprocal relationship.
Tests of intercessory prayer show no effect.
There is no good justification, assuming a benevolent and all-powerful God, for "natural evil," the suffering of animals and innocent children due to diseases and natural disasters. Theologians' attempts to explain why, for example, children get leukemia, why ten million civilians met their deaths at the hands of the Nazis, and why thousands are killed by tsunamis, are laughable, and not remotely convincing to anyone who hasn't already bought into religious delusion.
Earlier "evidence" for divinity has been dispelled (creation, Adam and Eve, Great Flood, etc.)
A benevolent God would not kill off humanity in 5 billion years. Nor would a benevolent and powerful God use evolution or natural selection to create modern life and humans. That just doesn't make sense, though theologians concoct amusing arguments not only why evolution makes sense, but why it should be God's preferred way to bring species into being.
There is no explanation for why a benevolent God would allow more than 99% of the species he wanted to exist to subsequently go extinct without issue.
Most of the universe inhospitable to life, and nothing lives there. Why this largesse of uninhabitable space if God created Earth for humans? Even if life exists elsewhere, it can't be common, and the trillions of uninhabited stars serve no purpose.