Because there is neither a 12:00 am, nor a 12:00 pm. One is 12 noon, the other is 12 midnight.

AM and PM are "ante meridian" and "post meridian": before" and after. But 12 is on* the meridian; neither one. You can meaningfully say 12:00:01 am, or 11:59:59 pm, but for 12 sharp nobody can say whether am or pm is dark or day.

Airlines schedule flights at 12:01 for this reason.

This is the reason 24hour clock is the way to go. 23:59, 00:00, 00:01, ...

0 was invented for a reason. This am/pm stuff is so confusing.

Meridian in this context is noon. 12 “anti meridian” is 12 hours before noon. 12am. Which is exactly correct.

I’m no domain expert but I’m guessing flights are scheduled at 12:01am because people are bad at time. For instance some people would think 12am is the last minute of the previous day instead of the first minute of the next day. 12:01 removes the potential ambiguity.

Nitpick but since we’re talking about time: AM means “ante meridiem”, as in “before”. Not anti as in “against” :)

You've just completed GP's point perfectly though - 12 hours after noon (post meridian) is midnight too.

12 "post meridian" is 12 hours after noon. 12pm. Which is midnight. But you don't use 12pm to mean midnight. Why not? Midnight doesn't actually belong to a day at all. Our current conventions of 12am and 12pm seem to be mostly products of digital time keeping.

OU4483 leaves CPH at 1200, as does another flight.

There isn't a flight at midnight, but there are fewer flights then anyway, and it may be confusing to some which day the flight is on. Of course, the flights around midnight have departure times of 2350 and 0015.

Wot, what's the false case?

DST. Some countries (Brazil) switch over at midnight instead of 2:00 am. One day of the year has no midnight.

I never considered how many logical problems arise from the use of AM/PM. I knew time handling is tricky but it seems like every time I see this topic discussed, I learn about a new corner case.

Some cultures end the day at (wait for it...) sunset.

And now we're back to the original problem.

Apparently Muslims and Jews here have agreed that the day ends at sunset or at 21:00, whichever comes first (or at all). It would be difficult if you couldn't eat for the better part of a month.