The term "nut case" is a slang expression that refers to a person who is irrational or crazy. There are many synonyms for this term, ranging from mildly derogatory to outright offensive. Some of the milder alternatives include phrases like "eccentric," "loony," or "unusual." Slightly more insulting synonyms might include "crackpot," "loon," or "wacko." More extreme alternatives might include terms like "psycho," "lunatic," or "maniac." Of course, it's always important to remember that such labels can be hurtful and dehumanizing, and it's important to treat all individuals with kindness and respect, regardless of any perceived mental health issues.