Another way for skeptics to dispel this notion would be to pick the UFO cases that come closest to meeting a skeptic's criteria for proof, explain why they come closest by citing the cases' strengths but then, in an amicable way, explain why the cases still ultimately fall well short of proof by citing the cases' pivotal weaknesses.
Probably the most common argument I come across — and this applies to other believer classes as well, such as 9/11 demolition believers — is that there isn't one "smoking gun" piece of killer evidence, but that
we must consider the totality of evidence over the past 75 years. And,
debunkers are pseudo-skeptics because they deny this mass of evidence. It's essentially "evidence by a thousand cuts," this idea that 100 pieces of weak evidence, or 500 pieces of very weak evidence, somehow adds up to strong evidence.
Even here on Metabunk we had a
user doing a Bayesian analysis involving a large number of UFO observations that he falsely characterized as independent events. The interdependency of the events is, of course, part of what makes all of the weak evidence not add up to strong evidence. But toward the end of the thread
he wrote, "My problem with Carl Sagan's 'Extraordinary claims require extraordinary evidence' is that it squashes each individual paranormal claim without allowing a group of good cases to be combined to offer support for the paranormal."
For years I watched the TV show
The Curse of Oak Island, because it was a good look into the believer mentality as well as a wall-to-wall critical thinking exercise. The cast members were constantly waiting to come across what they called "The One Thing": one piece of definitive evidence of treasure buried on the island. Meanwhile, all the little supposed clues (a scrap of parchment here, coconut fibers there, buried wood dated to the 1500s, etc.) kept their faith going that they would eventually turn up The One Thing.
While we all wait for The One Thing in UFOlogy, it's hard to say what single pieces of evidence are best. Gimbal? The schoolchildren eyewitnesses? Lake Cote? From my perspective anyway, they're all terrible and don't come close to the requirements that have been suggested in this thread.