I'm an atheist...

[Tiberius]

Translating to mathematics (or logic)

P: There is evidence for fairies
Q: We can say that fairies exist for sure

P => Q (P is a sufficient condition for Q, as Q is a necessary condition for P)

We know for sure that P is false, right?
But even then, there is no logical, rational way to get from there to a point when we can say anything about Q.

Bad use of logic.

P => Q means that P is a sufficient condition for Q, but not vice-versa. Just because someone (or all of us) can say "fairies exist for sure" doesn't mean there is evidence for them.

Indeed, if we "know for sure" that P is false, then Q *is* false by definition.