Extraordinary claims require extraordinary evidence
"Extraordinary claims require extraordinary evidence" was a phrase made popular by Carl Sagan. Its roots are much older, however, with the French mathematician Laplace stating that: "The weight of evidence for an extraordinary claim must be proportioned to its strangeness." Also, David Hume wrote in 1748: "A wise man ... proportions his belief to the evidence", and "No testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous than the fact which it endeavors to establish." and Marcello Truzzi says: "An extraordinary claim requires extraordinary proof."
Either way, the phrase is central to the scientific method, and a key issue for critical thinking, rational thought and skepticism everywhere.
The evidence put forth by proponents of such things as gods, ghosts, Neolithic bluestone quarries, the paranormal, and UFOs is highly questionable at best and offers little in the way of proof. Even if we accepted what evidence there is as valid (and it is highly debatable if we should), limited and weak evidence is not enough to overcome the extraordinary nature of these claims. (I added the bit about the quarries…..)
Alice and Bob are two friends talking after school. Alice tells Bob that she watched a movie the previous evening. Bob believes her easily, because he knows that movies exist, that Alice exists, and that Alice is capable and fond of watching movies. If he doubts her, he might ask for a ticket stub or a confirmation from one of her friends. If, however, Alice tells Bob that she flew on a unicorn to a fairy kingdom where she participated in an ambrosia-eating contest, and she produces a professionally-printed contest certificate and a friend who would testify to the events described, Bob would still not be inclined to believe her without strong evidence for the existence of flying unicorns, fairies and ambrosia-eating contests.