Why did the feudal medieval system emerge from the migration period that followed the fall of the Roman Empire?

After the fall of the Roman Empire, Europe stayed without the protection of the Roman army, and groups, known as Barbarians, like Huns, Visigoths, Vandals, Angles, Saxons, and Vikings, started invading western Europe. Those groups were characterized by being agressive and warlike; for that reason, people had the necessity to protect themselves, and they set up a new system known as feudalism, which was about rights and obligations to take care of the land ownership.

In other words, as common people did not have the protection of the Roman Army, they had to move towards wealthy and powerful lords to be protected by the Lords' private army, and as a payment, they looked after the land and the animals.

Feudalism, as a social and political system, emerged in the Early Middle Ages, and it was instituted in Europe for various centuries. Following the fall of the Roman Empire, the once mighty centralized power started to weaken and to be unable to protect the population, which had become increasingly more rural and had started to live scattered. Since it was now necessary for this population to get their own protection (against Barbarian invaders, bandits and rebellious peasants, among others), the feudal grant was conceived. By this grant, the free man ceded his land and his freedom to a noble man, who, in turn, offered him safety and protection. The common man had to work the land and produce enough to feed the noble and his family, as well as his own family and even the clergy, who did not work the land. In addition, he had to be able to go to war - or to send someone that could fight on his behalf. The noble men, in turn, pledged allegiance to a more powerful lord, and this one pledged allegiance to the monarch, who, finally, sworn allegiance to God.