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?
Yes, I didn’t quite calculate how controversial the topic would be, my bad…
I think the clear answer is that there is no real reason other than habit and sunk cost fallacy.
See also the metric system, A4 paper, and daylight-saving time.
I’m not Mexican, but this reminds me of a Mexican ranchera that says “No cabe duda que es verdad que la costumbre es más fuerte que el amor” (There is no doubt that it is true that habit is stronger than love).
There may have been some historical event that lead to this convention dominating over others (though I don’t really know where to start lookin)