As for the traditional Western gunfight as depicted in movies, the inaccuracy of handguns at the time would have made quick-drawing skill irrelevant: It was simply so unlikely you'd hit a guy on the first, second or third shot that it didn't really matter which guy got out his gun first. The closest history got to high-noon show downs was dueling, where people just stood across from one another with their guns out, aimed and fired until someone got lucky, and someone else was dead. Forget about "fanning," rapidly cocking a single-action revolver between rounds like Clint Eastwood does in A Fistful of Dollars. You'd be lucky to hit a henchman if the duel took place in a closet.
Why Do We Believe It?
Because famous gunfighters like Billy the Kid wanted you to believe it. If you've seen Young Guns on cable, you probably know the guy was gunning somebody down every ten minutes!
"... then I was all like 'pow' 'pow' and all the minotaurs exploded!"
Well according to sources who aren't Billy The Kid, his lifetime kill count was four. Criminals inflated their murder stats for the same reason guys today inflate their sexual experience: It made them look cool. Towns like Deadwood talked up their violent, lawless natures in order to attract adventurous settlers. Books were written about them and movies were made as soon as cameras were invented, and nobody who'd been out west was rushing to correct the misconceptions because, why the hell would they. A century and a half later, we still love that lie.