It’s not hard to see how monarchy came to be, Spandrell suggests:
Lands are conquered through war. Armies need a commander, so when an army conquers a piece of land, the commander becomes king. He rules and collects taxes which he funnels to his war brothers, who become noblemen.
Then the king dies. What happens? Well different peoples had different systems to arrange for succession for a ruler. What would happen in most armies when the commander dies, is that the generals will get together and choose one of them as the successor, if the king didn’t arrange for it himself. And that evolved into elective monarchy. Problem is it’s hard to get people to agree to choose one king. The stakes are too damn high. So what you got was all the contenders gathering their armies in anticipation of the king’s death, and total war among the elite every 10 years or so.
The solution which was most widely adopted was that of hereditary succession. The metaphor for the kingship changed, from that of commander of an army, to that of owner of property. Since time immemorial property of all kind has been inherited in the family; in patriarchal societies it would be inherited by the sons. And so most kingdoms eventually adopted the system of hereditary succession. The king dies, the son takes over.
What if there’s more than one son? Well, the inheritance of property itself has two sorts of arrangements. To this day, some people divide their inheritance more or less equally onto their sons. And some give the whole estate to the eldest son, and screw the others. There are pros and cons to both approaches. Partible inheritance tends to break up the estates, which become ever smaller and smaller, and eventually not very profitable, which is bad for the family name, and makes them prone to be bought up or taken by richer, stronger people with bigger estates. Primogeniture ensures the estate doesn’t shrink, and with it the family honor. But it creates a huge incentive for the younger brothers to kill the eldest.
Partible inheritance was popular in medieval Europe. But it eventually disappeared, for obvious reasons. If there’s only one guy who doesn’t do it, and keeps his big estate, he’ll be able to field a larger army and take the small estates that your oh so egalitarian father left you. And so we see that on most of the world, primogeniture monarchy ended being the most widely adopted system.