Celibacy originated in Apostlic times and is part of practical instructions in the way the Lord Jesus willed His Church to be organized that he left with the Apostles. Feudalism has nothing to do with it.
Celibacy was always the preferred state in life, even for the laity. The first “nuns” were widows who brought their property to the Church. Even married bishops were supposed to be celibate after election. This was a vein of Jewish religious observance unlike that of the Rabbis.
However, The mandated celibacy of the priest was a reaction to the corruption of the Dark Ages, when the monks provided a moral and intellectual contrast to the “secular” laity. The main aim, of course, was to insure that abbots and bishops remained celibate as they are in the Eastern Churches to this very day. That was because in the west, the nobility were the chief landowners, and the principle of monarchy was weak. The principle of celibacy made it harder for a noble to be elected as abbot or bishop, gain control of the lands, and pass it on to his issue.
This was a big deal since the lands of the Church were 10% or more of the whole and which the Church used to fund the social services its provided for the people, and this wealth was a tempting target for greedy nobles. It was a wealth that depended not just on alms but also the production of monastic estates , which regularly produced surpluses. Monasteries were run more efficiently than other estates, even the rich places scorned by St. Bernard and other reformers.