Why do we say "Marching to a different drummer"?

Meaning:

To follow your own path and to live/behave in an individualistic way.

Background:

This expression traces to a passage in Henry David Thoreau's 1854 work, Walden: "If a man does not keep pace with his companions, perhaps it is because he hears a different drummer. Let him step to the music which he hears, however measured or far away."

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