Of course there was a reason to divide the day in half, and that is, half the day the sun is shinning and the other half it is dark.
The initial time keeping had 12 hours of daylight and 12 hours of dark in every day. The problem with that is the length of the hour changed with the season, for example, in the winter the day hours were short as they had to squeeze 12 of them into what we now consider about 8 hours.
Eventually the hours were rationalized into equal sizes, but that lost the light/dark division. However, the AM/PM was retained for some reason, probably to minimize confusion.
What I find amusing is complicated wrist watches that have the seconds, minutes, hours, date, day of week, phase of moon, but yet they neglect anyway of distinguishing AM from PM.