Okay I understand from earlier articles why we have 24 hours in the day, and that “midnight” isn’t part of either day. And that some of these questions are easier with a 24-hour clock. But I don’t believe I’ve heard why the new day starts at 12:00 instead of 1:00.
Let’s day it’s Monday evening. 9PM, 10PM, 11PM…and it’s still Monday. But “12” becomes “AM” an it’s nowTuesday? Why isn’t 12 still part of Monday? Why doesn’t Tuesday AM start at “1”, back at the beginning of the counting cycle?
Because the real way it happens is that Midnight starts the count from 00:00, and you count up from there. 01:00 is the end of the first hour of the day.
Just like we count age; you don’t start out 1 year old, you know.
So the question on a 12-hour clock is what to call the times during that first hour of the day, and the first hour of the afternoon. By convention, we continue to number it as the hour which has happened after 12 such hours have already occurred. But the middle of the night happens at 12, so the new day starts at that point.
Isn’t 12PM really called Noon, or Midday? And 12AM really called Midnight? I believe it’s done that way precisely to avoid thorny questions such as this.
Doesn’t really solve the problem the OP has, though. Even if 12 is “really” midnight, the first minute after midnight is 12:01, not midnight:01. And the OP wants to know why it’s 12, not 1.
Just switch to the 24-hour clock and you could avoid these issues. 
Does that really explain it? Since we’re not on a 24-hour clock, there doesn’t seem to be an inherent need for a 'zero hour" as such.
Why can’t
12:59 to 1:00 be the last minute of Monday, and
1:00 to 1:01 be the first minute of Tuesday?
I’m not saying this is ‘right’ or ‘wrong’; I’d just like to know how and why it got the way it is in the first place.
It had to be something, and that’s what it was.
It certainly could.
However, when someone asks for the time, it is given as “x hours since midnight”. So, when you ask what time is it, and I say 2:15, it’s obvious that 2 hours and 15 minutes have elapsed since midnight. In your system, 2:15 would mean that 1 hour and 15 minutes had elapsed since the start of the day - hardly intuitive, wouldn’t you say?
Unless you are Chinese. According to Chinese traditions, you are one year old as soon as you are born.
“1 o’clock” means one hour has passed - literally “one hour on the clock” since the starting point. And we measure time from noon (when the sun is at its highest) or midnight (when the dark is directly overhead ).
Noon, when the sun is at its highest, is an obvious point to mark the day. So noon by definition is the middle of the day, which makes midnight the beginning of the day. It’s a simple as that.
Another way that it could have been different is the following:
We started with the decision that midnight is the time that the sun is lowest in the sky and noon is the time that the sun is highest in the sky. (Well, we can’t directly see that the sun is lowest in the sky at midnight, but that’s the idea.) In any case, it’s exactly a half day away from noon.) We decided that days begin at midnight. We decided that the time between midnight and noon will be divided into twelve hours, as will the time between noon and midnight. We decided that the point exactly one hour after midnight (and exactly one hour after noon) would be called 1:00, the point exactly two hours after midnight (and exactly two hours after noon) would be called 2:00, etc. We decided to split the hours into sixty minutes. Thus one minute after 1:00 is 1:01, two minutes after 1:00 is 1:02, etc. We can do the same thing for 2:01, 2:02, etc., 3:01, 3:02, etc. The question then is what we call one minute after midnight, two minutes after midnight, etc. (and the equivalent thing for noon).
We could have decided that one minute after midnight, two minutes after midnight is 0:01, 0:02, etc. Indeed, that’s how it’s done in certain sorts of 24-hour clocks. Instead we decided that these times would be called 12:01, 12:02, etc. This may not be quite as consistent with other mathematical formulations, but it’s how we decided to do it.
We certainly wouldn’t want to go back and then declare that 1:00 AM is the beginning of the day and 1:00 PM is halfway through the day. We’ve already decided that midnight is the beginning of the day and noon is halfway through the day. Changing that would mess everything up. The real problem is that the day starts with 12:01, 12:02, 12:03, 12:04, etc. instead of 0:01, 0:02, 0:03, 0:04, etc. (and the same thing for the times after noon). That’s the odd decision we’ve made.
For the same reason your life starts at birth instead of on your first birthday.
Well, the nautical day (at least in British tradition) used to start at noon. And that made sense because it’s the one point during the day that can be easily measured with fairly simple tools.
I suppose they could have counted the hours from 0 to 11 instead, but the whole concept of 0 is not very intuitive and I seem to recall from other contexts that people were somewhat prejudiced against it.
This is one area where we don’t need change. I like it the way it is…
Days used to begin at sundown, following the Judaic tradition, in most western societies. Christians were not as bound to this tradition, just as they changed the day of rest from Saturday to Sunday.
But the real reason midnight became the day’s start was because it was convenient. You have to change the date at some point. Why not pick the point when almost everybody was in bed, not conducting business, not engaged in government, etc.
With a midnight start, you can start the work day early in the morning, at sunrise or even before, work all day long, to sunset or even beyond, and everything you do falls on the same date. That makes the record-keeping much simpler and less confusing for future reference.
Astronomers today find this system a real pain, so they’ve invented substitutes that lump the entire nighttime period together. Astronomers are not thick on the ground, though, and never had much clout in government. Businessmen were everywhere and had enormous clout. Which group would you propitiate?
The system of starting the calendar day at sunset, as noted above, is very old, and continues today among Orthodox Jews and the liturgical churches (“anticipated Mass” on Saturday nights counts as part of Sunday for this reason).
But Wendell’s post cogently explains why midnight in particular was chosen for the beginning of a new calendar day: The middle of the day is of course midway between sunrise and sunset, when the sun is highest in the sky – i.e., local noon. If this is the middle of the day, it obviously begins and ends one half day off from that, i.e., at local midnight. Now add in the complications of standard time zones and daylight savings time, and you have the modern system in simple terms.