On a personal level, I was raised by atheists, so I was never indoctrinated into any religion, and have always approached all religious claims from the “outside”, rather than as things I have been taught to accept but must now find reason to reject. Of course, that’s more or less “insufficient evidence”, but just to tell you where I’m coming from.
Why I don’t believe in the God of Christian fundamentalists (Biblical inerrantists): I don’t believe in the God of those Christians who claim their God has inspired the Bible as his inerrant word because I find the Bible to be self-evidently errant, in that it has internal contradictions. It also contradicts other known facts of history and science, especially as interpreted by many Biblical inerrantists (a young Earth, separate creation of humans rather than human evolution from non-human animals).
Why I don’t believe in the God of classical Christian theology: The Trinity is a bit hard to swallow–probably not an insuperable objection; I’m willing to buy that light is both a particle and a wave, for example, even though I may not really understand it, because physicists have experimental evidence for wave-particle duality and other sorts of quantum weirdness, and I’m even given to believe that the working of my digital watch and my computer and all sorts of other gadgets can’t be explained without quantum physics. I have more insuperable objections to the classic problems entailed by the three omnis (omnibenevolence, omnipotence, omniscience), regarding the paradoxes of human free will, the problem of evil, and the internal contradictions between the various attributes of God–the problem of God’s free will, for example. Finally, I have problems with the dual natures of Christ: I don’t see how a God of the sort described by Christian theology, as above, can become man. If he’s omnipotent and omniscient, it’s meaningless to say he’s “fully human”. If he “empties himself” of those attributes, I don’t see how he can be said to be fully God. I could see Zeus voluntarily giving up his power to hurl thunderbolts for a time (kinda like Superman II) and still meaningfully being Zeus, but the Christian God’s nature is fundamentally omnipotent, omniscient, etc. An “incarnation” of God who doesn’t have those things isn’t really God; he’s just a man, even if he happened to have been born of a virgin by a supernatural act of the Holy Spirit. (This objection will not, of course, apply to Arian Christians.)
Why I don’t believe in the Judeo-Christian God in general: And probably for the gods of other religious traditions, it seems all too obvious to me that these are human-invented concepts which have evolved out of ancient societies trying to understand the Universe. They’re very historically rooted, and one can all too easily trace their evolution from earlier gods–a primitive storm god or battle god of a particular tribe becomes the Creator of the entire Universe, with many lofty philosophical and ethical refinements, but there are still many traces of the old tribal idols, the theological equivalents of the vermiform appendix or “junk DNA”. All the gods I’m familiar with show every sign of having been invented, not discovered.
Why I don’t believe in some sort of Intelligent Designer: It largely just boils down to the standard “lack of evidence”. (For, say, the Greek pantheon, it’s mainly just an argument from absurdity–that the Universe is ruled by a bearded Greek guy who cheats on his wife simply strikes most people these days as silly. Not a strong argument logically, but no one seems to really be making the case for Homeric fundamentalism, so there’s little need for anyone to come up with strong objections to it.) There is also a sense to me that the argument from design, the “watchmaker God”, is a rather overweening degree of anthropomorphism: the Universe is not a watch. Modern science, especially evolutionary biology, seems to reduce the need for a God; at the very least, almost everything but the simple fact of existence as opposed to non-existence can be pretty well explained scientifically, or at least plausibly hypothesized about: why the stars shine, why the seasons turn, and where humans come from. I also see no evidence that the Universe was made for us, and much evidence that it wasn’t: the Universe is mostly empty space; the parts which aren’t empty space which we can see are overwhelmingly not centered on us–as my signature points out, this is a pretty obscure planet. (And apparently even all the stuff we can see may be only a fraction of what’s in the Universe; whatever “dark matter” is, it seems to be cosmically more important than the stuff we see around here.) Most of the Universe is alien, hostile, and on really inhuman scales of space, time, and violent energy. Even locally, Jupiter is as big as all the planets put together (and I believe Saturn is as big as all the planets put together besides Jupiter). Earth’s a pretty small piece of debris. Of course, Earth is the home of life, and nowhere else that we know of is. But life on Earth is billions of years old; the dinosaurs lasted for hundreds of millions of years longer than we’ve been around, and the dinosaurs were recent. We are recent, and may yet just be a flash in the pan. As far as the argument from morality, the Universe seems a pretty cold and uncaring place, and life especially seems to have been driven from the beginning by blind, very amoral forces–survival and reproduction at all costs, leading to many things which would be (by our standards) disgusting, cruel, or depraved.
All of that doesn’t logically preclude a creator, of course, but it provides an argument against an anthropomorphic, personalized creator–even against the Deistic God who endows us with certain inalienable liberties and whose Providence governs the affairs of human beings.
I’ve tried to explain my conviction that God is quite real and present often enough, and been faced with people attempting to demonstrate the logical fallacies lying behind it, that I’ve all but given up on explicating my faith – I merely try to show that I’m doing what my Lord commands, and what I feel to be the right thing to do, and hope that’s enough.