Why do Americans want to know the month first and the day second?
I'm sorry but it doesn't make sense TO ME. Based on what I was taught, regardless of the month, I think what matters first is to know what day of the month you are in, if at the beginning, in the middle or at the end of said month. After you know that, you can find out the month to know where you are in the year.
What is the benefit of doing it the other way around?
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.