It is quite simple, actually: that there are phenomena that we cannot explain —such as moments or events that run the gamut of the fortuitous, accidental, absurd, miraculous, paranormal, or otherwise inexplicable—does not in itself justify our attributing a cause or explanation of any kind to these phenomena. If we concede the simple and credible assertion that human existence is filled with all kinds of inexplicable phenomena, then the only reasonable response to these phenomena is—no response, nor the attribution of any definite cause.
We are then in a position to undertake an orderly and rational process of investigation, hypothesizing, and testing, and any conclusions arrived at should remain at all times falsifiable. This is the criterion of science, where even the most apparently incontrovertible facts are still open to being controverted as a result of new discoveries, data, or findings.
This is also to say what a simple Latin phrase has already set out for the general betterment and stability of humankind (or to save us all from absurdly irrational flailing): Onus probandi incumbit ei qui dicit, non ei qui negat (the burden of proof lies with the one who speaks, not the one who denies). The sentiment of this phrase is buttressed by the more modern Sagan standard (after the lucid and broad-minded Carl Sagan), distillable to the aphorism that “extraordinary claims require extraordinary proof”.
These standards can be applied more broadly to any kind of dogma that gives a definitive set of answers or attributes a set of definitive causes to a set of inexplicable phenomena. Think creationism as an explanation for the creation of the universe. Can we disprove that the universe was created by a god that gave it order and coherence ex nihilo? No, but neither should we consider that explanation as having as much validity as, for example, the more tenable Big Bang Theory. While it is falsifiable (as are all scientific theories), the Big Bang Theory is much more credible than the idea of an omnipotent man-in-the-sky because it is the result of fleshed-out theorizing rather than imagining.
In the case of paranormal phenomena—for instance, demonic possession—we are again before a set of phenomena for which their proponents and espousers have provided some pretty dubious explanations. I would, of course, be happy to see proof of these phenomena beyond the merely anecdotal and see the wildest creations of directors such as William Friedkin take on actual life. But, unsurprisingly, this kind of proof is very difficult to come by. At one time or another, for better or worse, it seems we all have to come to terms with the uncertainty of existence.
