Personally I can get behind YMD and DMY (while sticking to ISO would be preferrable for obvious reasons), but what on earth possessed people to come up with MDY?
I have no idea why it started that way, but in everyday speech we say dates with the month first. So that makes MDY just the thing everybody is used to.
Fortunately the ISO format YYYY-MM-DD still has the month before the day, so I don’t have to worry about my fellow Americans getting it confused.
You know, I thought about it after reading the comments here, and I’ve thought of one possible explanation for MM-DD-YYYY, that being the order you effectively get the useful information from a date.
Going by DD-MM-YYYY, you read the first part, and that tells you the day in a month, but not which month, just skimming that first section gives you no actually useful information about how near or far it is without reading the second.
Doing MM-DD-YYYY on the other hand, you first read the month, which immediately tells you what part of a year it is, and if it’s relatively sooner or later, and then reading the second part of the date just gives more precision, rather than the whole useful answer.
So basically, it makes it easier to skim dates within a year with more useful information listed first, whereas putting the year first would just delay or offset that same skimming method.
Day first gives a range of error between 0 and roughly 330 days without reading further, whereas month first gives a range of error of only up to 28 to 30 days depending on the month.