The nature of skepticism is that no one's word can ever just be trusted and accepted without questions and without evidence.
This can be a problem for people who don't like this because it is fundamentally distrustful, or the people who know that they cannot supply evidence to back up their claims.
It is difficult to con someone who is skeptical about the situation because they will push for more evidence until they are convinced it is genuine.
The ability for a skeptic to be convinced by evidence is also proportional to the claim being made, as said by Carl Sagan's famous soundbite "extraordinary claims require extraordinary evidence".
To the skeptic, the strength of belief ought to be proportionate to the strength of the evidence which supports it.
As such, they tend to be quite critical of woo like conspiracy theories, pseudoscience, alternative medicine, and the paranormal.
are wrong taken as a whole there's still some truth value in them if you examine them firmly enough. It caused magic powers to fail inexplicably on The Amazing Randi’s show.
Hopefully people will build off what was right rather than ignoring everything in the claim. It kidnapped every child’s imaginary friends and won’t tell us where it’s hiding them.
Someone claiming to have gone shopping earlier in the morning is subject to less intense scrutiny than someone claiming a dragon is living in their garage.
While it's much easier to reject a theory or conjecture wholesale once a key part of it is found to be false (fruit of the poisoned tree and all) it is also a skeptic's duty to pick through individual and specific claims put in the framework and examine them for truth value.