Why is this language *not* pumpable? (language = arbitrary word followed by exact same arbitrary word)(pumping lemma for context-free-languages)
Some strings in your language are pumpable, others aren't. You have to look for one that isn't pumpable. Use the fact that the relevant piece is of limited length.
In your case, say the pumping length is $N$, and take $\sigma = 0^N 1^N 0^N 1^N$. You'll find that however you position the part that gets pieces repeated, you won't be able to increase the first and second stretch of $0$ or of $1$, or get the correct repeat by pumping around one of the $0/1$ boundaries.