This is what I was told. Priests could marry until about the year 1000. First, it was the church’s hierarchy that could not marry (cardinals, bishops, etc.) and over time, local parish priests were included in the single life. By about 1000, all priests, from the upper hierarchy to local priests, were single. This tradition started, as suggested in another posting, over land rights (property). In the day and age of arranged marriages between royalty, wealthy persons, or those of rank, if a priest married a woman of wealth, or the priest somehow became wealthy, and the priest died, the inheritance would go to the priest’s widow or children, and, hence, not to the church. The church was losing potential income. Therefore, if a priest were to remain unmarried, any wealth or inheritance the priest might gain would more likely go to the church and not to his wife, children, etc. The church later created a theological rationale about priests marrying the church as a justification for their financial motivation. It follows the old political adage: If you want to know what’s really going on, follow the money. I was told this by a retired Jesuit priest.