Similarly, people will claim it makes no sense that American M/D/Y dates are neither monotonically increasing nor decreasing, but then they'll find it totally natural to use "D/M/Y H:M:S" or "H:M:S D/M/Y" and not even notice that they share that same alleged flaw.
I'm just glad that nobody in Europe seems to use YYYY/DD/MM. This means that the format "YYYY-MM-DD" is unambiguous and the lexical ordering of dates is the same as their natural ordering[1], which is useful for sorting files in folders.
[1] Except for years BCE which the scheme doesn't treat.
"They" really don't. Either way you described is still either sorted in ascending or descending order: H:M:S D/M/Y (321 123) or D/M/Y H:M:S (123 321), as opposed to using MDY, which is neither ascending nor descending, but 213.
Additionally, the point of doing it the other way round is that the most important thing is on the left, where we start reading, followed by less important things. If I need to know the time of day, the hour is the most important thing, once I know whether it's 4 or 6, I can look at the minutes and first then do I perhaps (and does one really ever?) care about the seconds. As a matter of fact, my old wristwatch only had hour and minute hands... The opposite is true for the date. It starts, again, with the most significant thing on the left: the day. This assumes that people will probably have it easier to remember the month or year they live in.
And a final example: I have an appointment on the 24/01/2014 at 10:15:00. The most important questions are: What day do we have? And if it happens to be the 24th, what hour of the day is it? Is it 5? Good, 5h left. Is it 10? Oh boy, better look at the minutes...
I think you mean 321 456. It's not monotonically anything.
> most important thing is on the left
See, I feel that the month is the most important part of the date. "My birthday’s in June" or "My birthday is on the eight of some month"? "The harvest is in October" or "The harvest is on the 30th of something?"
When you are asked what date it is, do you think hardest about the month or the day? For most people it's the day, so it makes sense for it to come first.
The hour. Minutes are usually unimportant for day to day life, as long as I am in the right hour. This is not true of month-day though. I imagine most people would be caring more about day than month. The day is both more important and harder to remember, so it makes sense for it to come first.
The hour. Is this supposed to be a trick question? 90% of the time, if I give the hour to quarter-hour resolution then I've done a good enough job of saying what time it is. I don't even think about minutes.
