Assume the hypothetical set of all sets is called X, and that it contains the elements (a,b,c). Now copy it, call the copy Y, and insert the copy into the original set. X now contains the elements (a,b,c,Y). Notice how inserting Y into X alters the set such that Y (a,b,c) is no longer identical to X (a,b,c,(a,b,c)). The logical implication is that Y is no longer accurately described as a copy of X. No matter what we do we can never create a set that contains itself. 

It might be possible to imagine a set that contains an infinite ammount of sets, all possible sets in fact. But defining it such that it needs to contain itself, you have turned the idea into something self-contradictory.
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