Words can be like people. Some will always look on the bright side, while others take a more pessimistic view of things. Words that fall into this latter category possess what linguists call "negative polarity." Don't worry, this is not a severe psychological disorder but an entirely harmless grammatical condition, with no reported side-effects whatsoever, that means some words and expressions prefer to show up in negated sentences.
A textbook example is the adverb あまり(amari). If you don't feel hungry and would like to qualify this a little bit, you could say あまりお腹が空いていない (Amari onaka ga suite inai, "I'm not very hungry"). However, even if you should, in fact, happen to be quite hungry, you cannot turn this into a positive statement as it stands. Though あまり is not impossible in non-negated environments, there are adverbs much more suited to strengthening an affirmative sentence. Try, for instance, 大変 (taihen), とても (totemo) or, more casually, めっちゃお腹空いてる (Mecha onaka suiteru. I'm very/totally hungry).
A similar case of negative polarity afflicts 必ずしも (kanarazushimo, necessarily). Let's say you don't agree with what someone said but want to make sure your disagreement won't come across as too direct. Then you could say 私は必ずしもそう思わない (Watashi wa kanarazushimo sō omowanai, "I don't necessarily think so"). Be careful not to confuse 必ずしも with the slightly shorter 必ず, which has no medical record of negative polarity, and in contrast, predominantly occurs in positive sentences.