To drive away or chase something, usually by waving your hand; an exclamation used to make someone or something go away.
From Middle English, possibly imitative in origin, similar to words like 'shush' that mimic the sound of pushing something away. The word has been used since at least the 16th century.
Shoo is one of those words that sounds like its meaning—we use it to literally push away, making it perfect for commanding a cat to leave the kitchen, and it works across multiple languages because the sound communicates the action.
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