On the contrary, the Catholic Church holds that a sacramentally valid marriage is indissoluble. This does not mean that a validly married couple cannot get a civil divorce (civil divorce in itself has nothing whatever to do with a sacrament); but it does mean that, even if a civil divorce is obtained, the validly married husband and wife are still married in the eyes of God, and cannot remarry until the other partner dies.
Annulment is a different matter: it is not divorce. It is based on an investigation of the validity of the sacrament and the vows. If both the husband and the wife made sincere vows (they weren't drunk, crazy, immature, coerced, mentally handicapped, ignorant of the meaning and obligations of the married state, etc.) and were truly free to marry (there was no question of incest, bigamy, etc.), the bond stands; but if the vow was null (defective) from the git-go, there was no indissoluble bond. Hence annulment: a finding of no marriage.
I would be truly grateful to be corrected on this subject, but my understanding is that the Orthodox Church under some circumstances permits divorce and remarriage, even if the couple was validly married in the beginning. That's what my divorced/remarried Orthodox friends tell me.
Please direct me to some link if I'm wrong about this. I'm here to learn.