The phrase "fly off the handle" means to suddenly become very angry or lose one's temper. The origin of this phrase is rooted in the literal image of an axe head flying off its handle, which would occur if the tool were poorly constructed or not properly secured. 

The phrase likely originates from the 19th century in the United States. When an axe head flies off its handle, it does so unexpectedly and violently, much like a sudden outburst of anger. This imagery effectively conveys the idea of losing control in a sudden and potentially dangerous manner. 

The first recorded use of the phrase dates back to the mid-19th century. The American humorist Thomas C. Haliburton used it in his book "The Attaché; or, Sam Slick in England" published in 1843. Haliburton wrote: "He flies right off the handle for nothing."