This expression probably refers to the tendancy of a man who is about to fight to take his shirt off before fighting (this might not be the case today, but in the days when most people had only one or two sets of clothes it would have been prudent to protect them!).
In 1854 it was used in The Spirit of the Times by George W Harris who wrote "I say, you durned ash cats, just keep yer shirts on, will ye?"
Note: 'Keep your socks on' was also considered a correct answer in this quiz.
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