Actually, MM/DD/YYYY is in the minority worldwide. AFAIK, only the US and Canada use it.
All of Europe uses DD/MM/YYYY (Germany uses dots instead of /) and I believe most (if not all) of South America too.
Chinese and Japan effectively use YYYY-MM-DD because of how it's written normally, YYYY年MM月DD日. A lot of the tech and business world also use YYYY-MM-DD because it's an ISO standard, and makes sorting easier if you assume left-to-right reading order.
However, there are two interesting observations:
* Most of the world reads left-to-right, but uses Arabic numerals which is right-to-left. So, most of the world uses big-endian Arabic numerals when in the original language it was little-endian. Also strange that when we say "Arabic numerals", we also don't use their numerals, only their system...
* The difference in US date formats compared to the rest of the English speaking world boils down to how the dates are spoken. In US English, it's typical to say e.g. "January 10", whereas in British English this is practically unheard of. But this explains why to an American "MM/DD" feels more natural. In Britain, sometimes people might say "January the 10th", but "10th of January" is far more natural. This is why we prefer "DD/MM" because it's a natural abbreviation. You can still see vestiges of the earlier British-style usage in US English, e.g. "4th of July" which is ironic for the date that should be least British is pretty much the only one that's still said the traditional British way!