impertinent
Rude and disrespectful, especially toward someone in charge.
Impertinent means rude in a way that shows a lack of respect, especially toward someone in authority. When a student gives an impertinent answer to their teacher, they're crossing a line into disrespect by being sarcastic, dismissive, or inappropriately bold.
The word often describes behavior that ignores proper boundaries. If a younger sibling tells their parent, “You can't tell me what to do,” that's impertinent. If someone makes a joke at exactly the wrong moment, like laughing during a serious conversation, that might be called impertinent too.
What makes something impertinent involves both what you say and your tone and timing. Asking a reasonable question politely is fine, but demanding an answer in a snippy voice is impertinent. The word captures that specific kind of rudeness where someone acts like rules of respect don't apply to them.
Impertinent is similar to insolent, though insolent suggests even bolder, more aggressive disrespect. When someone calls your behavior impertinent, they're telling you that you've forgotten your manners and crossed into genuine rudeness.