Cold Shoulder
. To show or give one the cold shoulder is to assume a distant manner towards a person, to indicate that you wish to cut his acquaintance. The reference is to a cold shoulder of mutton served to a stranger at dinner; there is not much of it, and even what is left is but moderate fare.
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Entry taken from
Dictionary of Phrase and Fable,
edited by the Rev. E. Cobham Brewer, LL.D. and revised in 1895.