While it's confusing and I prefer y-m-d over both of those, the American way is based on the way dates are said in spoken (American) English. Hence things like September 11th, 2001
(Indeed, this one specific date gets said the American way even in British English. We Brits don't do that for any other dates - we say "fourth of July" instead of "July fourth", for instance - but "September 11th" aka "9/11", uniquely among all dates, is written and said the American way in all dialects of English on the planet due to its significance to American culture.)