The supposed honor of being selected to do a difficult or unpopular task or the supposed honor associated with receiving a questionable award.(noun)
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Use "dubious honor" in a sentence
"Johnston's death left the command of the army to General Pierre Beauregard, who had had the somewhat dubious honor of firing the first shot of the war against Fort Sumter and of capturing the little garrison which defended it."
"Todd has the dubious honor of being from away, a non-Wheaton native."
"Bell had given Ned the dubious honor of commanding the rear guard against Doubting George's onrushing army."