"Presumably, it's the latter, due especially to the Canons of Trent, Session XXIV. The teaching against divorce (with its attendant focus on annulments) is incredibly well-established. It would be tantamount to a change of course in, say, teachings about the papacy, for example. That is to say, while some might welcome the change, the change itself would tend to undermine any claim to being "the Church" based on an exposed and clear lack of consistency."
For a Catholic, the Council of Trent is an ecumenical council and therefore its teachings on divorce, as they touch on morals, are infallible, directly inspired by the Holy Spirit, unchangeable.
If you say Trent is wrong then you are acknowledging that it is not really an ecumenical council after all and, if it wasn't, what about all of the other so-called post-schism ecumenical councils? To invalidate one ecumenical council or one teaching of faith and morals of an ecumenical council is to potentially invalidate them all.
If you say it was right then, but wrong now, then you would be saying moral truth can change, that the Holy Spirit can change His mind.
But if it really is an ecumenical council and its teachings on morality are therefore infallible and unchangeable, then how do you explain what is currently happening at the Vatican? That the pope, either by his action or inaction, is defying what he knows to be the express will of God and leading others to do the same? Two other supposedly ecumenical councils, Vaticans 1 & 2, say that, if I'm Catholic, I have to obey him on matters of faith, morals, discipline, and governance even when not speaking infallibly. Are those teachings of faith of an ecumenical council false?
When you get right down to it, it's Orthodoxy, sedevacantism, moral relativism, or denial. I really don't see a plausible alternative.