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?
The short answer is, it’s what we were taught in school. Like many preferences, it’s shaped by the culture we grow up and live in.
Of course not, you were raised and live in a different culture; so, your preferences are different.
Ultimately, the right answer is ISO8601. It’s unambiguous and sorts well on computers. But, I don’t think any culture is teaching that as the primary way to write dates, so we’re stuck with the crappy ways.
There is an American subculture teaching and using ISO 8601; the US military. They don’t call it that, but I learned later that’s what it is. They enforce YYYY-MM-DD on all documents.
YYYYMMDD is commonly used throughout East Asia.