Full Idea
Sets, unlike extensions, fail to correspond to all concepts. We can prove in ZFC that there is no set corresponding to the concept 'set' - that is, there is no set of all sets.
Gist of Idea
ZFC can prove that there is no set corresponding to the concept 'set'
Source
A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.4)
Book Reference
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.90
A Reaction
This is rather an important point for Frege. However, all concepts have extensions, but they may be proper classes, rather than precisely defined sets.