In a word is an idiom. It means, roughly, "As a short, pithy, description, I will say...". Idioms are not expected to be literal, especially since most of them are metaphors.
In a sentence, however, is just an ordinary prepositional phrase, is not an idiom, and has no special or metaphorical meaning, and thus must be interpreted literally. So it has no particular reason to appear in this sentence, since You are wrong! -- like practically every other utterance -- is already, and obviously, in a sentence. In a sentence, what else is new?