As others have noted, the current incarnation of dry fly fishing has been around since the 1800s, but the argument of which is the "right" way really started to get elitist in the early 1900s.
This is an enjoyable web article on a bitter battle that took place 100 years ago in the UK.
http://midcurrent.com/history/halfor...he-both-of-us/
And the battle persists...