To throw one's hat in the ring - Idiom of the Week
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As defined in Linda and Roger Flavell’s book Dictionary of Idioms and Their Origins, “to throw one’s hat in the ring” is an idiom that means “to issue a challenge; to proclaim one’s candidacy” (page 150).
“My hat’s in the ring. The fight is on and I’m stripped to the buff.” – Theodore Roosevelt, February 21, 1912, Cleveland, Ohio
In the beginning of the 19th century, anyone that wanted to challenge a boxer to a gloveless or bare-knuckled fight would physically throw their hat into the boxing ring. This would capture the attention of the onlookers.
The phrase then evolved to a more general climate, applying to contests or competitions of various kinds, most specifically political candidacy (page 150).