The Wikipedia page on Russell's paradox states
if $R$ were a normal set, it would be contained in the set of normal sets (itself), and therefore be abnormal; and if $R$ were abnormal, it would not be contained in the set of all normal sets (itself), and therefore be normal. This leads to the conclusion that R is neither normal nor abnormal
We have to assume that there are such things as extraordinary or "abnormal" sets for this paradox to be valid. The solution to the paradox is to change the definition of a set so that it cannot include self-referent collections.
Why do we assume that sets must be normal or abnormal in the first place? To my eye this whole thing can be avoided if we do away with what appears to be an unnecessary assumption.