Hello, Anonymous. Sorry you think my answer is terrible, but often there really is no reason for why we say things one way and not another. "Nonexistent" is a word. "Unexistent" is not a word. On the other hand, "uninteresting" is a word and "noninteresting" is not. We can tell you what English speakers say and don't say. Sometimes we can give reasons, or rules, but not always.