Legacy reasons

That's it

When you speak it, do you say July 3rd or 3rd of July? Both are fine.

I wondered whether maybe the us americans had continued using the old style and it was Britain that changed, but no: Britain appears to have been using the day-month-year order since medieval times. This latin letter from William Wallace from 1297 has that order: https://www.wikitree.com/wiki/Space:Lubeck_Letter

*Given at Haddington in Scotland on the eleventh day of October in the Year of Grace one thousand two hundred and ninety seven. *

The latin line with the date starts with "datum".

I was taught DD/MM/YY and that's what I use in typed form, but I prefer MM/DD/YYYY, at least in speech e.g. 'June 13th 2025'. It feels cleaner to narrow by month, then day, otherwise you're mentally having to wait for context, working backwards. The year is almost irrelevant as it changes so infrequently, about once a year.

ISO 8601 for organising on a computer, as sorting by largest to smallest is the most logical.

The US is the only one to do many stupid things, like imperial units

Many computer systems store dates starting with the year. Isn't that interesting?

Linguistics

In UK English, it's considered proper to write "the 6th of March" as "6 March" and sometimes read as "6th March" which can be jarring to Americans as their shorthand is "March 6th" and when "6(th) March" is encountered in written form, it's expanded to the full "6th of March" when spoken

That doesn't mean this won't be yet another feature American English absorbs from UK English but right now flipping them in speech requires a few extra syllables and people are lazy

In Chinese, its also Month, then day.

Its always "五月 三十一号" (May 31st), never "三十一号 五月" (31st May)

When saying a day in history, the full format is used: 一九六九年 七月二十日 (1969 Year 7th Month 20th Day), but when you use it during every day life to refer to a day in the same year, the year is omitted. If you are referring to the same month, the month also get ommitted.

TLDR: Not unique to "Americans"

We don't want or care about it. Its just the way its always been over here. Same with fahrenheit and the imperial system. I know this is a little exaggerated but imagine asking a Japanese person why they dont just speak english because its the worlds most spoken language. Its one of those things other countries like to pick on us for that I think is a little stupid. Instead you should be dunking on us for putting an orange party clown in the whitehouse. Again. But then again there are some exploitative processes that helped make that happen like gerrymandering. My point is that our shit healthcare and the majority of the things that we are laughed at for is out of our hands. Even the fat jokes can be somewhat blamed on the fact that the availabilty of cheap unhealthy food with a large portion size is greater than pricier organic options and lots of the poor tend to take that route. I'm not saying our majority is completely blameless but these are factors to consider.

Edit: following your Edit: thank you for the clarification