Why did people allow feudalism to happen?

People had no choice. If you were born into peasantry or serfism, you were there for life unless you became a priest. You couldn't fight the king or the lords or knights. The kings got a ton of power and no one could do anything to stop it. The only people with enough power to not allow it to happen were the kings and they didn't want it to stop.  It is much like how the 1% in USA is getting way richer and more powerful because we, as the middle class, can't do anything about it.

Because the lords were protecting them from outside attacks in exchange of their labor, which in those times wasnt pretty much if some person is trying to kill your family...