Why is the language of even-length non-palindromes context-free?
The language of even-length non-palindromes is given by the following context-free grammar:

$$S \rightarrow 0S0 \mid 1S1 \mid D$$
$$D \rightarrow 1A0 \mid 0A1$$
$$A \rightarrow \lambda \mid 00A \mid  01A \mid  10A \mid  11A$$