I’m sorry but it doesn’t make sense to me. 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?
Idk, maybe like all U.Sians traditions, this was an Old-World British thing Americans preserved, since it’s a more direct term of the English language, more direct than Day then Month
so unless it’s a special day, if not holiday, for U.Sians like 4th of July, by default, Month then Day