なかなか～ない

なかなか in front of a negative verb means "not easily", "just won't": something you want or expect keeps not happening. The verb is in its negative form, and the tone is impatience or mild frustration.

Without the negative, なかなか means "quite": なかなかいい is "pretty good".

Your own actions take the potential

When the action is yours and you are trying, the verb goes into the potential before ない. A plain negative would sound as if you are choosing not to.

• × 私は漢字をなかなか覚えない → 私は漢字がなかなか覚えられない

なかなか～ない or あまり～ない

あまり with a negative just means "not very", "not much". なかなか needs something you are waiting for or working at, so it doesn't go with a plain description.

• × この本はなかなか高くない → この本はあまり高くない