Wikipedia

You're correct, it says so in the article further down, It's not a paradox in the "formal" sense, it's only a paradox in the sense of what intuitively would be considered evidence, but in actuality isn't, I'll try to give an easier example to demonstrate use of actual basic logic.

Claim: "all natural* numbers are even".

• Natural: whole number which is zero or greater. (Zero not always included, blame mathematicians)

1. Notice that pointing at a natural number which doesn't contradict the claim, isn't evidence, and that exists infinitely many natural numbers who don't contradict the claim (2, 4, ...), yet 1 does, and is considered evidence to the contrary.

2. Notice that pointing at a non-natural number, which doesn't satisfy the claim, also isn't evidence, also in this case there are infinitely many such numbers (-1, -3, ½,...).

Also as a demonstration, let's invert the claim formally, we swap "all" with "exists", and invert predicates: "exists a natural number which isn't even", this inverse is useful because it can point to how to disprove the original claim, because there exists such a number (1), i can say that i proved the inverse of the original claim, this is equivalent to disproving it.

Tldr: the paradox is a short exercise in how formal logic differs from naive intuition, there isn't really a paradox.