Why do you think the vassals had to swear an oath to remain faithful to the king?

The Vassals had to swear oath to his lord. Fealty means the duties of a vessel for his king. It included the swearing for remaining faithful to the lord, the act of homage preceded it. In act of homage the vassal used to kneel before the lords and placing his hand in the hands of the lord promised to stay loyal . The oath took place upon a religious object such as Bible. fealty and homage were the key elements of European feudalism. Fidelity is different from the other parts of homage as is refers to that part of ceremony where the vassal swore to be a good vassal to his lord.

The Vassals oath was a  promise not to harm his lord or damage his property, it was a recognition of the assistance owed by the tenant to his lord and the protection owed by the lord to the tenant.