Dividing the solar day into 12-hour days and 12-hour nights is a very old notion. We have sundials and water clocks from ancient Egypt and Mesopotamia with 12-hour divisions. They date to 1,500 BC or older, so the reason for choosing to split the day in this fashion is kind of lost to us. We don’t have texts specifically explaining why they did it.

But it’s not hard to see why they might have. The 12-hour cycle comes from the Sumerian numbering system, which uses base 60. Since there are 12 moon cycles (months) in a year, there is also pre-existing significance to the number 12 in time keeping.

Splitting the solar day also makes sense. The diurnal cycle has huge impact on humans. You work in the day, sleep at night. You can see stuff in the day, you don’t see well at night. The sun comes out in the day, the moon and stars at night. These are all big, significant things, so it’s not very surprising that time keeping systems acknowledge this division.

This is quite separate from the question of counting hours. Whether you continue to count to 24 or repeat the count after reaching 12 is different from the idea of having 12-hour day/night cycles. You can have both. There are ancient Egyptian, Mesopotamian, Chinese and Indian clocks with 24 hour days. And in fact, the earliest mechanical clocks in Europe also had 24 hour mechanisms. The clock face might be marked from 1 to 24, or 1 to 12 twice, or both. But the clock mechanism operated on a 24 hour cycle.

In practical usage, a lot of Europeans did switch to counting in 12 hours with AM and PM added, especially since the late middle ages when mechanical clocks were invented. This is because in the early days, people didn’t have watches or clocks in their homes, they told time by the striking of the hour from the big clock in the church or town hall. These old clocks were driven by weights suspended on ropes running over pulleys.

The thing is that if a clock only counts to 12 and then repeats, it has to strike 78 x 2 = 156 strokes per day. But if it counts to 24, it has to strike 300 times per day to count off 24 hours. Striking more times means having longer ropes and taller clock towers, or heavier weights and more pulleys to gear the mechanism down, all of which cost money. That’s why lots of towns opted for 12 hour clocks, and the people simply followed suite. If you hear the bell strike 3 times and it’s not the middle of the night, it must be 3:00 PM and not 3:00 AM. On a 24 hour clock, it would have to strike 15 times for 3:00 PM, which takes a lot more rope.

Of course, astronomers have always preferred 24 hour time, regardless of the number of bells. And modern militaries too, because there’s less chance for ambiguity. For average people, it varies by country. From my understanding former parts of the British empire stuck with 12 hour time the longest, while others switched to 24 hour time earlier.

A good source for this stuff is the book History of the Hour: Clocks and Modern Temporal Orders by Gerhard Dohm van Rossum. Published by the University of Chicago Press in 1996.