Although there are people who will sometimes say:

1. Today is Thursday, the 24^th of May, 2012.

There are also others who instead say the same thing this way:

2. Today is Thursday, May 24^th, 2012.

Certainly in the United States, the second way of mentioning a date is more common than the first. The long form sounds more formal to us, as in “on the Fourth of July” being more formal and long-winded than simply saying “on July 4^th”.

It was pronouncing the month before the day out loud that gave to retaining that same original order when converted to digits: merely convert the month name to a natural number, and there you have your answer. What’s today’s date? It’s May 24^th. Instead of writing May-24, we simply change the “May” to “5” and write 5-24 or ⁵⁄₂₄.

That way it follows the natural language order and so requires no mental gymnastics to switch things around when speaking the date aloud. Similarly “September 11^th” gets written ⁹⁄₁₁, etc.

The full spoken form with the year, “May 24^th, 2012”, then becomes the written shorthand “5/24/2012”, or often just “5/24/12”. “Christmas of 2001” can be, and somewhat annoying often is, written “12/25/1”, while “January 25^th, 2012” becomes “1/25/12”.

This isn’t usually any sort of problem because of universal consensus on how to interpret such things in the United States. If you write day/month/year in America, you will not be understood. Although I myself prefer the ISO notation, normal people do not use it in their daily affairs.