I've been silently ruminating for several days now. Admittedly, I hesitated to say anything because the upvotes my answer accrued finally permitted me to reach that mythical 10k milestone. But, after careful consideration, I believe that the OP posted their question on the wrong Stack Exchange site.
It's patently clear that the OP wanted a technical, not a language, explanation.
Every new answer offers the same computer engineer's mindset; the same concepts, point out the same discrepancies in the 12-hour clock, and completely fail to focus on the English language aspect. Undeniably, no one topped tchrist's splendid opening paragraph for its breadth and deftness.
What you see with “11 ᴀᴍ + 1 hour == 12:00 ᴘᴍ” is largely an artifact of the way we keep time with a zero-based system on computers per ISO 8601, and what happens when you map a zero-based 24-hour time like 00:00:00.00000 into a 12-hour ᴀᴍ/ᴘᴍ time, which is one-based.
But as admirable as tchrist's answer is, as well-written as it is, was the Original Post really a language poblem? How helpful are its answers to learners? As an example, I offer another snippet of @tchrist's answer
Alas this confusion of ordinals and cardinals starts young, back when we first teach our toddlers how to count items. When you number items using ordinal numbers, you have a first item, then a second item, then a third item. We teach our toddlers to start with one, two, three instead of with zero, one, two. The concept of zero is more complicated than a two-year-old needs. If you with perfect accuracy tell them they’re in their third year instead of in their second year when they’re “two years old”, they won’t understand you. That certainly won’t make sense to them then, and for some it may never make sense.
That paragraph is introducing the reasons why midday and midnight are historically represented as 12:00. Although, I'd argue, if you take away a two-year old's chocolate cookie and tell them they have zero cookies, the concept of "zero" becomes crystal clear. But I digress.
The question attracted a slew of other "technical" answers. For example,
@CJ Dennis's answer
In mathematics, a number range can be represented as:
(0-12) zero to twelve, not inclusive
[0-12] zero to twelve, inclusive
(0-12] zero not inclusive to twelve inclusive
[0-12) zero inclusive to twelve not inclusive
The parentheses ( & ) indicate that the adjacent number is not inclusive, i.e. that it is excluded from the range. The brackets [ & ] indicate that the adjacent number is inclusive, i.e. that it is included in the range.
here's a snippet of @kwah's answer (bolding not mine)
Given this pattern of all other times after noon and before 1PM having the PM suffix it is, therefore, common to (incorrectly) assume that 12:00 noon also needs to be labelled PM but, as shown above, this is not the case.
and @Rob's answer
Solar time is directly derived from the Sun's position, by counting one hour of time every 15° of hour angle as Earth is rotating around its axis in 24 hours, which gives 360°/24 h = 15°/hour. So, 15 * 12 = 180, thus half a circle measures 12 hours.
the Romans got mentioned a couple of times, for instance in @aij's answer
You have knowledge that the Babylonians and Romans did not have. They did not know of this strange number 0.
12 is congruent to 0 (mod 12), so XII is the number the Romans had that made the most sense between XI and I.
@David K's answer
But place-value systems typically allow any of their digits to be zero. In binary, as you count up each digit changes from 0 to 1 and then to 0 again; in decimal it goes from 0 to 1 and so forth up to 9 and then to 0.
When telling time, the minutes and seconds also follow this rule: after 59 we have 0. But the hour is an exception: the next hour after 12 is 1. Worse still, the change in the date doesn't occur then, but occurs one hour earlier, between 11:59 pm (one minute before midnight) on one day and one minute after midnight on the next day.
The ELL help centre says questions should be about the following (emphasis mine)
- Word choice, usage, and meaning
- Dialect differences
- Spelling and punctuation
- Pronunciation and accents
- Other practical problems you encounter or face while learning English
To sum up, and crystallize my hamletic dilemma, is the OP's question
If Why is 11 am + 1 hour == 12:00 pm? off-topic, what should be done?