On the topic of marriage as a sacrament from the earliest times, Peter Lampe notes the origin of the practice by which the Roman church operated outside of civil rules for marriage: "...it is crystal clear in Hippolytus that from aristocratic circles more women than men found their way to Christianity. The disproportion was a social problem that Callistus during his term as Roman bishop (c. 217-22) attempted to solve. The problem undoubtedly had existed since the end of the second century, if not longer.
When women from the noble class were unmarried and in the heat of their youthful passion desired to marry and yet were unwilling to give up their class through a legal marriage, he [Callistus] allowed them to choose a partner, whether slave or free, and to consider him to be their husband without a legal marriage. From that time on the alleged believing women began to resort to contraceptive methods and to corset themselves in order to cause abortions, because, on account of their lineage and their enormous wealth, they did not wish to have a child from a slave or a commoner.From Peter Lampe, "From Paul to Valentinus: Christians at Rome in the First Two Centuries," pg 119.
A Christian woman [from a wealthy family] who wished to retain the title "clarissima" had two options. She could marry a pagan of the same social status and forego marriage wtih a socially inferior Christian. Or she could live in concubinage with a socially inferior Christian without being legally married. This second option received the blessings of Callistus in Rome. In this way he prevented two things: mixed marriages with pagans and the social decline of Christian women. Both were in the interests of the community. (121)This is why Rome can say that it has mastery over marriage -- why, even though a couple may take vows, have any number of children, ask for and pay for an annulment, and voila, "the marriage never existed."
And that's why they can say they don't permit divorce. Because if they were to use the usual sense of the language, then they would have to admit that Callistus's end-run around the usual definition of what was a legal marriage was really an instance of permitting unmarried couples to live in sin. And of course, the pope is infallible. So they're stuck defending this set-up.