Men, whose worldview by definition already denies the possibility of a supernatural being beyond himself, tries to define such a being, and upon failing to do so fully to his liking, concludes that said being clearly does not exist. God is comparable to a math equation in which the answer, rather than having a well-defined numerical answer possibly with a few decimal places, is instead, "the limit does not exist." God is boundless and while we know parts of his character, parts of the equation, when trying to solve the problem, in the end the only result we can come to is that His limit does not exist. Certainly no mathematician would demand a student to find another suitable solution to the problem, that IS the solution! Even more, nobody would consider attempting to discredit mathematics as being fallacy. There is such a thing as something being defined as undefined.
The means by which some men make this attempt to solve this problem and explain God already set them up for failure. They limit His existence and His character to man-made rules based upon what we "know." But how can you prove a supernatural spiritual being exists when by default your rules already deny that possibility by limiting it to a physical realm? Think about it: A thought is some kind of electrical transmission; a memory, a reaction between neurons; neither of which we fully understand nor can we pin down a physical location in the brain where memories are stored, yet nobody doubts that man can think and can remember. Is a memory physical or is it something else? If it is just physical, why can't we extract a memory from the brain like we can extract an organ or a blood sample? Maybe it's not just physical, maybe it's something more... But if one tries to argue that God is "something more," then well it's just a bunch of fanatical religious mumbo-jumbo! And we have scientists who claim to "examine the evidence" but in reality they are merely stacking the deck, so to speak, against what they already believe to be false.
Don't hear what I'm not saying. All this is not to say that there is not scientific evidence supporting the existence of God, more specifically the claims of Christianity. There are scientists who know much more than I that make extremely convincing argumentsscientifically for the existence of God. But that's not my goal here, my point is a philosophical argument, not scientific. (I find the Kalam cosmological argument to be especially fascinating, myself)
A quote comes to mind, although I'm not sure who said it: "God created man in His own image. And man, being a gentleman, returned the favor." We have an obsession with anthropomorphism. We define our universe in relation to ourselves. We characterize life through a very human, very mortal looking glass. The world is defined in man-made terms and what something "is" or what we think about it often depends on how it relates to us. God certainly does reveal himself to us in anthropomorphic images to help us, with our feeble minds, to understand His infinite character. But as soon as we LIMIT Him to just that, we deny any possibility of knowing Him further.
Isn't it reasonable to expect that a supernatural being that exists in some way beyond His creation and thus is far greater than it, call Him God, would in some ways be beyond mortal man's understanding? A being such as this would be impossible to define in terms of man. Why SHOULD He reveal Himself completely to us? And even if He were to do so, who is to say we would even be able to comprehend it?
The good news is that for those that choose to believe, God WILL reveal Himself and He WILL be fully known. The apostle Paul writes in 1 Corinthians 13:12 - "For now we see in a mirror dimly, but then face to face. Now I know in part; then I shall know fully, even as I have been fully known." I sincerely believe we were not meant, in our present state, to know God fully. It would be too much, we couldn't handle it. But I also sincerely believe God has revealed enough of Himself to warrant belief... even if we don't know it all.