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Theory I heard: Irish step dancing derives from Lancashire step dancing, where the arms are held loosely. Lancashire step dancing was traditionally judged by someone sitting under the table on which the dancer was dancing, so the arms weren't involved.
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I'd suspect all the explanations are apocryphal. Most likely, I'd argue, is simply that it's visually interesting, and human nature leads us to try and push any art to the edge of its envelope.
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