Murphy v. Burns in 1913, a pretty much inconsequential boxing match ended when Burns’ corner threw a towel at the referee to get him to stop the fight. Murphy was pounding this man’s face relentlessly. The crowd was begging for the fight to end. Burns would not quit, and finally the towel got the referee’s attention. The newspaper referenced this act of throwing in the towel and shortly thereafter was picked up in a few silent movies. Thus was born the phrase.
This was not a new concept. In the 18th century, bare knuckle fighting often led to sponges being used to mop up the blood on someone’s face. Throwing up the sponge was a common way to say that this is getting so bad, we just give up.
In contrast, you can also throw your hat in the ring. This is a very similar, but related concept that has the absolute opposite meaning. Throwing your hat in, means you are ready to jump into the fight, as opposed to giving up.
Sometimes I wonder. Am I getting ready to throw in the towel, or throw in the hat? Not sure.