Arrogantly tells you how someone does a thing: in that “I am above you” way. A person may speak arrogantly, smile arrogantly, wave away help arrogantly. The word does not name the person; it names the manner. It is a little more at home in writing and careful speech than in the playground, where people are more likely to say stuck-up or full of themselves. Same soft warning as arrogance: people sometimes reach for it when they only mean “too sure” or “not soft enough.” The feeling in the room still matters. If you use it, you are not only describing a voice. You are judging it.