Because it mirrors conversational American English.
In American English, at least conversationaly, it's natural to say it that way, so it's often written that way.
"What's today's date?", she asked.
In reply, he said, "Oh, it's February twentieth, two-thousand and six."
So that would be written as: Feb. 20, 2006, or 2/20/06.
I think the reasoning is that for at least the first 28 days of each month, all twelve months have a 1st, 2nd, 3rd, etc. so by putting the month first, you're immediately eliminating the question: "Which 20th is it?" In essence it's using the month as a adjective to the day. It's like saying: "A red apple."In English, putting certain adjectives behind the noun without a modifier or pronoun is awkward, it's like trying to say "A apple red."
It's not unusual to say it day, month, year, either, but it's not quite as common.
"In reply, he said, "Oh, it's the twentieth of February, two-thousand and six." but you have to have the pronoun "of" in the sentence to link the adjective of the month to the primary noun of the numbered date. Of course, this isn't entirely accurate, as you could pick any portion of the date as the primary noun, such as using the year with day and month as the modifying adjectives too...
Anyway, that would write as: 20, Feb. 2006, or 20-2-06. Putting the date first in purely abbreviated or numeric notation might seem subconciously awkward to American English speakers since the "of" that can be there when written or spoken isn't there in purely numeric form.
If you hunt around in American documents and literature or computers, you'll find both formats, but month-first seems to dominate in the common parlance.