In other words, a Gentile couple who were also in-laws (e.g., a man who married who married his sister-in-law) might be married in the eyes of the pagans, but in the eyes of the early Church, they were engaged in porneia, fornication. This explains why a word ordinarily meaning fornication is used: fornication refers to sex between unmarried parties (that is, it's premarital, not extramarital), and so the term captures that there's no real marriage here.
This harmonizes Matthew's Gospel with Mark and Luke's: allowing divorce and remarriage where the marriage is invalid doesn't contradiction the absolute prohibition against divorce and remarriage.
Take a modern example: there are Catholic and Evangelical groups fighting to preserve marriage and stymie the divorce epidemic. Most of these groups are also against gay marriage, and are naturally in favor of people getting civil divorces to get out of these sham “marriages.” It's not really divorce, because it was never really a marriage. There's no inconsistency here: both of these positions flow from the idea that, in a true marriage, God (not the state) joins the spouses together in a permanent and indissoluble bond.
My non-Catholic readers might not care about this last point, but my Catholic readers should. The Twenty-Fourth Session of the Council of Trent explicitly rejects (and condemns) the proposition that you can divorce and remarry, declaring it contrary to “evangelical and apostolical doctrine”:
This should make it clear: as Catholics, we don't need to worry (or hope) that the Catholic Church will change Her teachings in this regard, because She can't. She's bound by the words of Christ.
Much more could be said on this score, but hopefully, it's clear that the “infidelity exception” people claim exists in Matthew 5:32 and 19 does not actually exist. So for all of those reasons, we can be sure that (1) Jesus didn't permit divorce and remarriage, even in cases of adultery; and (2) the Church can't permit divorce and remarriage, even in cases of adultery.
Joe Heschmeyer is a seminarian, former lawyer, and blogger at Shamelss Popery.