This little chestnut is commonly applied in two ways; first, that we shouldn't mock people substantially less famous or powerful than us. If you're a famous comedian, you don't use your platform to pick fights with some poor guy just starting out. The second way this advice is phrased is that we shouldn't joke about or use derogatory terms for groups who have traditionally been victimized, like people with mental difficulties, or gay or transgender people.
Or the Irish.
Which is all good and fine, and excellent advice to live by. But I don't know if the concept of "don't punch down" is adequately covering the problem.
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It's sort of creating a muffin top of the problem.