It's organized by information priority. The part of the year you are in is more important than the specific day of the month. It's more meaningful, for example, to say that "It's December ARGH" as you are killed than to say that "It's the sixth ARGH".
Both are more important the year, which has little impact on daily life.
For a proper logical order, of course, you can't beat 2002-12-06. This both allows it to match up with the methods for time (to use your example, you would not say 30:45:05 (30 seconds, 45 minutes, and 5 o'clock), AND allows count-based mechanical sorting to more easily resort dates.
However, that still screws up the order of information usefulness. With hours, minutes and seconds, the logical order just happens to match.