Those who believe in fairies, or miracles, or alien visitation, are generally fond of an argument called argument to the best explanation. Here's an example of argument to the best explanation (or abduction, as it's sometimes known):
I see shoes poking out from under the curtain and the curtain twitching slightly above them. I can also hear breathing. I infer there's someone standing behind the curtain. Why? Because that's the best available explanation of what I observe. True enough, the twitching might be caused by the breeze from an open window and the shoes were just coincidentally placed in the same spot. But I reckon that's a bit less likely than that there's someone standing there (for what explains the breathing noise?).
Quite what makes an explanation the ‘best’ is controversial, but there's some agreement that the simpler and more elegant an explanation, the better. So, for example, I could explain that twitching curtain by supposing that there are three dwarves standing on top of each other behind the curtain, but that's a far more complex and less elegant explanation for what's observed than that there's just a single person there.
We use argument to the best explanation a lot. For example, it's used by scientists to justify positing various unobserved entities. We may not be able to directly observe electrons, or a very distant heavenly object, but their existence can be the best explanation of what we can observe, such as certain astronomical or experimental results. In which case, we're justified in supposing these unobserved entities – electrons, distant planets, and so on – exist.
So argument to the best explanation seems to be a legitimate form of reasoning – a form of reasoning employed even by scientists.
However, argument to the best explanation is often also the first port of call for those who believe in spooky, wacky stuff.
For example, conspiracy theorists rely on it a lot. They say: ‘Can you explain why the Twin Towers came straight down like that? No? Well I can – it was a controlled demolition! An inside job! See – that's the best explanation!’ In reply, we may have to admit that we can't, right now, explain the striking way the Twin Towers collapsed. So, if the conspiracy theorists' explanation is currently the best available, shouldn't we accept it? Aren't they justified in supposing a controlled demolition took place?
Or suppose we can't explain the testimony of various supposed witnesses to a flying object. Suppose it's observed by a number of individuals who describe something like a large flaming object hanging stationary over a building site. They are otherwise reliable witnesses. We cannot easily explain what they saw in terms of it being a planet, or a plane, or a prank, or an illusion, etc. So it seems the best available explanation is that a large fiery object really was spotted in the sky, right?
‘You can't explain it – I can explain it by appealing to aliens, gods, ghosts, etc.; therefore my explanation is the best available, and thus the most reasonable!’ is a popular refrain from those who believe in spooky stuff.
This sort of move also crops up a lot in religious contexts. Take the Resurrection of Jesus, for example. Typically, this is argued for using argument to the best explanation. We are told Biblical scholars agree on certain facts: that Jesus' tomb was empty, that Jesus was seen afterwards by several different witnesses, and so on. And then it's suggested that a risen Christ is the best available explanation for these reports – a better explanation than that all the witnesses were lying, or deluded, or that Jesus had not really died, etc.
So what, if anything, is wrong with this sort of justification of belief in 9/11 conspiracy, alien visitors, ghosts, fairies, and even the Resurrection?