I work as an historian. The reasons that celibacy were imposed were actually much greater than that. It became one of the cornerstones of the famous “Cluny Reform Movement”, and was actually something of a grassroots reform. There were several problems with married priests. First, since education was so poor, the few priests that there were often had to perform Mass on a circuit that involved several manors. As a result, they wouldn’t be in the same place for very long. Their taxing schedule made being married and raising a family very difficult (and prone to affairs and the like). Secondly, there was the problem of some priestly families living a “high lifestyle”. On larger manors that could support their own priest, sometimes the family of the priest had a household that was almost as grand as the lord of the manor. Sometimes, wives or family members would also spend funds donated in to the church (there wasn’t really a collection plate back then, as they just had church taxes) on their personal lifestyle. The third, and arguably largest problem, was simony and nepotism. Priests had influence, and they could use it to give their sons an unfair advantage in gaining either secular or religious positions (frequently with bribes skimmed from the church’s tax money). Simony and nepotism were the greatest problems of that era, and the reason the reform movement started in the first place. It basically came to a head with the Investiture Struggle, where Henry IV of the Holy Roman Empire tried to appoint bishops and priests without the permission of the pope. This resulted in a ban on lay investiture as well, and much tighter rules for investiture by the clergy. Other reforms of the time included the College of Cardinals, and the beginning of seminaries (since many priests were poorly educated, and barely knew the faith themselves).