A blanket statement is a type of vernacular that would be spoken by people in a group (“blow out your candles,” “blow the candle,” “blowing out the candle”).
The term comes from old slang such as when someone would need to take cover from weather (like rain or snow) and have a blanket thrown over them. In this sense, they were taking shelter under a “blanket” of protection. But in modern slang, it can also refer to something said quickly without much thought – like trash talk among athletes before stepping onto the field or court for competition. The idea is that people should be prepared for verbal attacks coming at them fast and furious because someone has given up on respecting their opponent’s opinion.