Use this phrase to emphasize someone's peaceful nature without suggesting physical weakness or cowardice. My grandmother is so caring, she wouldn't hurt a fly.
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Non-literal Meaning
The phrase is not about flies. It's an exaggerated way to say someone is non-violent. He's a pacifist and wouldn't harm a fly.
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Emotional Emphasis
The phrase can also imply affection or protectiveness towards the person described. Don't yell at her; she wouldn't harm a fly.