impertinent

This term carries a sharp edge of social friction, describing a specific type of rudeness that challenges a hierarchy. It is not merely being mean, but specifically crossing a boundary of deference, often characterized by a cheeky or insolent tone. It is frequently used in formal or academic settings to describe a breach of etiquette.

In a legal or technical context, the word shifts entirely away from personality to describe a lack of logical connection. When something is impertinent to a case, it is an extraneous detail that does not contribute to the evidence, making it a synonym for irrelevant rather than rude.