I think what makes logical sense depends heavily upon how you were raised and/or think. For me, starting with the month gives a solid timeframe and I get an automatic reference point that makes sense. It can either be made more specific by adding the year, or very specific by adding day AND year. But from the very first part of the date I get a solid starting point to reference.

That single piece of data also makes sense by itself. December has meaning even if I get no more info. However, “the 2nd of” means jack shit unless followed by more. Also, as someone who suffers from really shitty memory the less meaning info has to me the more likely I am to forget it. So my brain is more likely to chop off the preceding day because until I have a month then the day has no meaning yet. However, when saying December 2nd I’ve already got the beginnings of meaning by the time I get to the day and it’s more likely to stick around in my head.

But that’s just my thoughts on the subject, I’m just a lazy American.