Why isn't the word phonetic spelled phonetically?

Answer 1

Because it comes from Greek "phonos" meaning sound. Words of Greek origin in English retain their "ph" or "x" (as in "xylophone") so as to be able to identify them as Greek words. Most of them are in science or the names of studies such as philosophy and psychology (there's another one, "ps").

The Greek letter phi, from which "ph" comes, is not pronounced "f". Put your lips together as if for a "p", open them slightly and make a blowing sound which is somewhere between "p" and "f" and you have it.

Answer 2

Probably for the same reason that the word palindrome isn't a palindrome.