Alvin Plantinga makes the case to Gary Gutting in The NYT's The Stone (image from Wikimedia Commons):
G.G.: You say atheism requires evidence to support it. Many atheists deny this, saying that all they need to do is point out the lack of any good evidence for theism. You compare atheism to the denial that there are an even number of stars, which obviously would need evidence. But atheists say (using an example from Bertrand Russell) that you should rather compare atheism to the denial that there’s a teapot in orbit around the sun. Why prefer your comparison to Russell’s?
A.P.: Russell’s idea, I take it, is we don’t really have any evidence against teapotism, but we don’t need any; the absence of evidence is evidence of absence, and is enough to support a-teapotism. We don’t need any positive evidence against it to be justified in a-teapotism; and perhaps the same is true of theism.
I disagree: Clearly we have a great deal of evidence against teapotism. For example, as far as we know, the only way a teapot could have gotten into orbit around the sun would be if some country with sufficiently developed space-shot capabilities had shot this pot into orbit. No country with such capabilities is sufficiently frivolous to waste its resources by trying to send a teapot into orbit. Furthermore, if some country had done so, it would have been all over the news; we would certainly have heard about it. But we haven’t. And so on. There is plenty of evidence against teapotism. So if, à la Russell, theism is like teapotism, the atheist, to be justified, would (like the a-teapotist) have to have powerful evidence against theism.
G.G.: But isn’t there also plenty of evidence against theism — above all, the amount of evil in a world allegedly made by an all-good, all-powerful God?
A.P.: The so-called “problem of evil” would presumably be the strongest (and maybe the only) evidence against theism. It does indeed have some strength; it makes sense to think that the probability of theism, given the existence of all the suffering and evil our world contains, is fairly low. But of course there are also arguments for theism. Indeed, there are at least a couple of dozen good theistic arguments. So the atheist would have to try to synthesize and balance the probabilities.