Because it's a strap and it's worn by jocks? Edit: That's a genuine reply btw, not a joke or sarcastic one.
A protector worn by riders, i.e. Jockeys. Jockeystrap - Jockstrap. Relatively simple, I would have thought.
Well....there was once a scotsman who used to be, shall we say, a bit frugal with the truth, who had a friend that invented a protective covering for the soft and dangly parts of the male anatomy whilst playing sport. His friend named the object "Jock's trap" because it is full of bollox....true story...
Invented in the USA for the protection for the cycle delivery riders. Jock was a the slang word meaning a mans you know what. So the name Jock strap became part of the English language...... (Or American as they seem to think they invented the language)
This is feeling a little like those panel games where you have to tell the truth from the fiction. Personally I don't think it is anything to do with the Scots or people who ride horses.