Context-free grammar for ${a^n b^n a^n}$
The languages of all palindromes  is context-free.

That does not implies that any language that contains only palindromes is context-free. For example, many language over the unary alphabet $\{a\}$ are not context-free. In fact, they can even be non-context-sensitive or undecidable. Note that any word over a unary alphabet is a palindrome.

In particular, the language of all words like $a^nb^na^n$ is not context-free. The rough intuition to understand why it is not context-free is that a PDA cannot remember two unbounded independent relations. You can either use the pumping lemma to prove that fact. 

Exercise. Give an example of a unary language that is not context-free.