Why isn't palindrome a palindrome?

Answer 1

Because it doesn't read the same way backwards and forwards. A word does not need to be an example of its definition.

Do you ever wonder why the word "abbreviation" is so long or why "onomatopoeia" doesn't sound like anything?

Answer 2

A palindrome is a word that reads the same forward and backward. The word "palindrome" itself cannot be a palindrome because it does not read the same when read backward ("emordnilap").