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?
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