Here's a common way in which people appeal to ‘mystery’ in order to defend theism against the criticisms of atheists.
‘Why does the universe exist? You, as an atheist, cannot answer this question. You must admit that it is a mystery that has not been solved. But if you do not know the answer to this question, then you cannot know that my answer – that it was created by God – is incorrect. You must admit that, for all you know, I'm right!’
This is a bad argument. Suppose Sherlock Holmes is having a bad day. He just cannot figure out who dunnit. Does it follow that he cannot reasonably rule certain suspects out?
Of course not. Holmes may not know who dunnit, but he might still know who didn't. He might be able pretty conclusively to rule out certain suspects (the butler, for example, who has a cast iron alibi). Similarly, someone unable to explain why the universe exists may nevertheless be able to use their powers of reason to rule certain answers out. Indeed, even a religious person will typically admit that there is overwhelming evidence the world was not created by an evil God. But then they must admit that there could be overwhelming evidence that it was not created by a good God either (personally, I think there is).
This point is by no means restricted to religious beliefs, of course. Wacky belief systems often start with a mystery – they offer to explain what might otherwise seem rather baffling. Those who believe there's a family of plesiosaurs (snake-necked dinosaurs that went extinct 65 million years ago) living in Loch Ness, that the world was once ruled by aliens who still visit occasionally, that there's a ghost in their attic, will point to peculiar shapes on the surface of the Loch, or the extraordinary ancient Nazca drawings in Peru (huge images only visible from high in the sky – some say they were created for the benefit of passing aliens), or exquisitely constructed crop circles, or the weird rattling sound coming from the attic, and say, ‘Explain that!’ They challenge us to explain how such things were formed, or how or why they were made. When we can't, they conclude their beliefs, which we may be forced to concede do actually explain these things, can't be so unreasonable after all.
But of course, whether or not we can explain such things, we might still have excellent evidence that there is no family of plesiosaurs in living in Loch Ness (for a start, the Loch has been frozen solid top to bottom many times over during the ice ages that separate us from the age of the plesiosaurs).
