Idiom: At the drop of a hat
OED definition: informal Without hesitation or good reason
Example: My little brother cries at the drop of a hat
This idiom stems from the days when men routinely wore hats. Hats were a fashion statement, and were also used to give different signals, for example, waving it in the form of a greeting or tipping it to say ‘hello’ to an acquaintance. The dropping of a hat is believed to have originated in America during the 19th century as a sign that a formal fight was about to begin. Although the original usage was mainly associated with bar fights, it has now come to mean any situation when a person acts quickly, without hesitating or when a person does something without just cause.
Interestingly, this isn’t the only idiom to have originated from men’s head accessories as several others also exist, for example, ‘throwing your hat into the ring’ to accept a challenge.