Celibacy was part of the Church's identity, as well as a strategy for keeping wealth within the Church. The American historian and Vanderbilt Professor Katherine Crawford writes that:
Celibacy set the clergy apart, and instantiated patristic suspicions about sexuality as weakness and distraction from God within the moral architecture of the Church. The Church benefited practically from denying clerics the right to pass on property to their offspring: the property of the Church did not diminish. As with the laity, sexuality for the clergy had pragmatic elements at its core.
- Crawford, Katherine. European Sexualities, 1400-1800. Cambridge University Press, 2007.
Although the question sought to set aside biblical reasons, realistically, people's actions throughout history have been influenced by their belief system. In this case, Christian scriptures provide ample ideological reasons for celibacy, and moreover treats chastity as a virtue.
Quite logically, therefore, clerical celibacy was adopted as a badge of the church's spiritual superiority over the civil society at large. The late Belgian theologian Edward Schillebeeckx states, for example:
Continence among the clergy demonstrated the church's distinction from society.
- Edward Schillebeeckx. Celibacy. New York: Sheed and Ward, 1968.
And:
Sexual continence was difficult to maintain, so the Catholic Church hit upon the idea of utilizing the celibacy of the clergy to mark both their separation from and their spiritual superiority to the laity ... Christians in Late Antiquity valorized sexual absitnence to such an extent that this became a marker of the spiritual elite.
- Crawford, Katherine. European Sexualities, 1400-1800. Cambridge University Press, 2007.
By the 4th century, the chastity of the priesthood was enough of a universal concern that it was a topic at the first ecumenical council, held in Nicaea.
However, the requirements for celibacy in that council did not forcibly invalidate the unions of married clergy. Instead, their wives were regarded to be above suspicion. The University of Reading Professor Helen Parish describes the Eastern interpretation following Nicaea to be:
[R]eferences to the third canon in the East, including fifth century Theodosian Code, tended to make explicit reference to clerical wives in the list of women with whom clergy could be permitted to reside ... At the second Council of Nicaea in 787, and in the views of later canonists, it was assumed that the third canon of 325 referred only to unmarried bishops, celibates and monastics, and was not intended in any way to limit the activity of married clergy and their wives.
- Parish, Helen. Clerical Celibacy in the West: c. 1100-1700. Ashgate Publishing, Ltd., 2013.
For obvious reasons, expecting married clergy to abstain from sex with their wives was unenforceable and widely ignored. This was particularly problematic because the Church had established celibacy as a core element of its identity. Although Eastern, and later Orthodox, Christianity continued down a moderate path, in the West reform-minded theologians were sufficiently troubled to be galvanised into action during the High Middle Ages.
That chaste marriage attained some popularity among the laity made claims for clerical superiority murky ... Recurrent complaints that clerics had failed to maintain celibacy (usually the children were the big tip off) led to efforts under the Carolingians to enforce it, but many priests lived openly with their wives or concubines.
Because the Church staked so much on celibacy, clerical sexual transgressions were a source of criticism.
- Crawford, Katherine. European Sexualities, 1400-1800. Cambridge University Press, 2007.
Sexual transgressions of the priesthood were thus, in modern terms, a public relations disaster. It was the need to address this situation that (with ample help from ideological biases) helped fulled a renewed push for strict clerical celibacy in the 11th century and later.
Gregory's actions against the married clergy did not come from concerns surrounding the purity of those who celebrated the sacraments alone. Gregory's rhetoric was laden with references to obedience and obligation, and the eradication of clerical incontinence, like the eradication of simony, was part of a more general attack on a base manner of life that undermined the reputation of the church.
- Parish, Helen. Clerical Celibacy in the West: c. 1100-1700. Ashgate Publishing, Ltd., 2013.
Married clergy were an obvious target for the reformers, who thus imposed increasingly forceful measures against clerical marriages in a bid to ensure clerical celibacy. Contrary to the impression of the question, however, clerical celibacy was not eliminated over night. The reforms were deeply and bitterly resented, and it took centuries for clerical marriages to go out of fashion.