Full Idea
The naïve view of set theory (that any zero or more things form a set) is natural, but inconsistent: the things that do not belong to themselves are some things that do not form a set.
Gist of Idea
Naïve sets are inconsistent: there is no set for things that do not belong to themselves
Source
George Boolos (Must We Believe in Set Theory? [1997], p.127)
Book Reference
Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.127
A Reaction
As clear a summary of Russell's Paradox as you could ever hope for.