The idea that extraordinary claims require extraordinary evidence is a nonsense because even if evidence was presented of an extraordinary claim being true it still wouldn't be believed- the observer would think they were being tricked, such as we expect a magician would do. For such matters no evidence would suffice if we believed that such a happening was impossible!
This is why many areas of human experience are disbelieved by skeptics. There is literally no evidence possible that is strong enough to convince them. Any evidence produced would be described as either too weak or an act of trickery. A skeptic wouldn't even trust their own senses if confronted with proof. That is why so-called extraordinary claims can never be proven to a skeptic's satisfaction if it disagrees with their strong disbelief!
Winston Wu's take on extraordinary claims requires extraordinary evidence can be read here.
Here is a sample:
Of course, skeptics have argued that all these things are possible but not probable, hence the requirement for extraordinary evidence. However, in order to really know all that is probable and improbable in the universe and reality, it would require that one have complete knowledge of every dimension and reality that exists in the universe and beyond. No one, neither skeptic nor believer, has that kind of knowledge, at least not consciously. Therefore, it would be more accurate to state that:
"Extraordinary claims require extraordinary evidence to convince skeptics, but not necessarily to exist in objective reality."
2) Definitions of "extraordinary claims" vary based on prior beliefs and experiences. Not everyone agrees on whether a claim is extraordinary or ordinary. Suppose we were fishes for example, and lived underwater our whole lives without ever seeing or hearing about land. The claim of land existing above water would be an extraordinary claim to us, though not to the creatures living on the land above. Now obviously just because the claim of land is extraordinary to us as fishes does not mean that the land doesn’t exist. The point is that extraordinary claims are not extraordinary to everyone. What is extraordinary to some is ordinary and natural to others depending on their experience and level of consciousness. For example, the internal body energy of chi gong (or quigong) is mystical to Westerners but has been a natural everyday part of life for thousands of years in Asia. Chi is used, felt, and observed by its practitioners much the same as the effects of gravity are felt and observed by us. Likewise, the concept of Astral Projections and Out of Body Experiences is extraordinary to those who have never experienced them, but for those who experience them regularly, it is an ordinary thing to them that they know is a reality. In the same way, our cars, radios and cell phones are extraordinary to tribal natives in remote parts of Africa, but ordinary to us. The best solution, in my opinion, is for everybody to put their cards on the table by honestly specifying their prior beliefs. This sets the standards for what is to be expected and leads to a better mutual understanding of each other.