Jesus elevated matrimony to the status of a sacrament. Thus any valid marriage between two baptized people is a sacramental marriage and cannot be dissolved. If anyone so married attempts to divorce and remarry, he enters a state of perpetual adultery (a mortal sin).
Jesus declared: "Every one who divorces his wife and marries another commits adultery, and he who marries a woman divorced from her husband commits adultery" (Luke 16:18, cf. Mark 10:11–12).
Paul said: "Thus a married woman is bound by law to her husband as long as he lives. . . . Accordingly, she will be called an adulteress if she lives with another man while her husband is alive" (Rom. 7:2–3).
These strictures apply, of course, only to sacramental marriages—those between baptized people. For marriages involving an unbaptized party, a different rule applies (1 Cor. 7:12–15).
Amid the Greco-Roman culture, which allowed for easy divorce and remarriage, the Church Fathers proclaimed Christ’s teaching on the indissolubility of marriage, just as the Catholic Church does today in our easy-divorce culture (cf. Catechism of the Catholic Church 1614–1615). Other churches have modified their teachings to accommodate the pro-divorce ethos that dominates modern culture, but the Catholic Church teaches what Jesus taught.
A baptized couple can "remarry" after divorce only if the Church finds that a valid sacramental marriage never existed in the first place (a decree of nullity; see CCC 1629). The "remarriage" is actually their first marriage. If, however, the parties were genuinely and sacramentally married, they may in some cases live apart and even to obtain a legal separation, but they are not free to remarry (CCC 1649). This is not a command of men, but one that comes directly from Jesus Christ. As Paul said: "To the married I give charge, not I but the Lord, that the wife should not separate from her husband (but if she does, let her remain single or else be reconciled to her husband)—and that the husband should not divorce his wife" (1 Cor. 7:10–15).
"What then shall the husband do, if the wife continue in this disposition [adultery]? Let him divorce her, and let the husband remain single. But if he divorce his wife and marry another, he too commits adultery" (Shepherd 4:1:6 [A.D. 80]).
"In regard to chastity, [Jesus] has this to say: ‘If anyone look with lust at a woman, he has already before God committed adultery in his heart.’ And, ‘Whoever marries a woman who has been divorced from another husband, commits adultery.’ According to our Teacher, just as they are sinners who contract a second marriage, even though it be in accord with human law, so also are they sinners who look with lustful desire at a woman. He repudiates not only one who actually commits adultery, but even one who wishes to do so; for not only our actions are manifest to God, but even our thoughts" (First Apology 15 [A.D. 151]).
Clement of Alexandria
"That Scripture counsels marriage, however, and never allows any release from the union is expressly contained in the law: ‘You shall not divorce a wife, except for reason of immorality.’ And it regards as adultery the marriage of a spouse, while the one from whom a separation was made is still alive. ‘Whoever takes a divorced woman as wife commits adultery,’ it says; for ‘if anyone divorce his wife, he debauches her’; that is, he compels her to commit adultery. And not only does he that divorces her become the cause of this, but also he that takes the woman and gives her the opportunity of sinning; for if he did not take her, she would return to her husband" (Miscellanies 2:23:145:3 [A.D. 208]).
"Just as a woman is an adulteress, even though she seems to be married to a man, while a former husband yet lives, so also the man who seems to marry her [and] who has been divorced does not marry her, but, according to the declaration of our Savior, he commits adultery with her" (Commentaries on Matthew 14:24 [A.D. 248]).
Council of Elvira
"Likewise, women who have left their husbands for no prior cause and have joined themselves with others may not even at death receive Communion" (canon 8 [A.D. 300]).
Council of Elvira
"If she whom a catechumen [an unbaptized person studying the faith] has left shall have married a husband, she is able to be admitted to the fountain of baptism. This shall also be observed in the instance where it is the woman who is the catechumen. But if a woman of the faithful is taken in marriage by a man who left an innocent wife, and if she knew that he had a wife whom he had left without cause, it is determined that Communion is not to be given to her even at death" (canon 10).
"A man who marries after another man’s wife has been taken away from him will be charged with adultery in the case of the first woman, but in the case of the second he will be guiltless" (Second Canonical Letter to Amphilochius 199:37 [A.D. 375]).
"No one is permitted to know a woman other than his wife. The marital right is given you for this reason: lest you fall into the snare and sin with a strange woman. ‘If you are bound to a wife do not seek a divorce’; for you are not permitted, while your wife lives, to marry another" (Abraham 1:7:59 [A.D. 387]).
"You dismiss your wife, therefore, as if by right and without being charged with wrongdoing, and you suppose it is proper for you to do so because no human law forbids it; but divine law forbids it. Anyone who obeys men ought to stand in awe of God. Hear the law of the Lord, which even they who propose our laws must obey: ‘What God has joined together let no man put asunder"’ (Commentary on Luke 8:5 [A.D. 389]).
"Do not tell me about the violence of the ravisher, about the persuasiveness of a mother, about the authority of a father, about the influence of relatives, about the intrigues and insolence of servants, or about household [financial] losses. So long as a husband lives, be he adulterer, be he sodomite, be he addicted to every kind of vice, if she left him on account of his crimes he is her husband still and she may not take another" (Letters 55:3 [A.D. 396]).
"Wherever there is fornication and a suspicion of fornication a wife is freely dismissed. Because it is always possible that someone may calumniate the innocent and, for the sake of a second joining in marriage, act in criminal fashion against the first, it is commanded that when the first wife is dismissed a second may not be taken while the first lives" (Commentaries on Matthew3:19:9 [A.D. 398]).
Pope Innocent I
"[T]he practice is observed by all of regarding as an adulteress a woman who marries a second time while her husband yet lives, and permission to do penance is not granted her until one of them is dead" (Letters 2:13:15 [A.D. 408]).
"Neither can it rightly be held that a husband who dismisses his wife because of fornication and marries another does not commit adultery. For there is also adultery on the part of those who, after the repudiation of their former wives because of fornication, marry others. This adultery, nevertheless, is certainly less serious than that of men who dismiss their wives for reasons other than fornication and take other wives. Therefore, when we say: ‘Whoever marries a woman dismissed by her husband for reason other than fornication commits adultery,’ undoubtedly we speak the truth. But we do not thereby acquit of this crime the man who marries a woman who was dismissed because of fornication. We do not doubt in the least that both are adulterers. We do indeed pronounce him an adulterer who dismissed his wife for cause other than fornication and marries another, nor do we thereby defend from the taint of this sin the man who dismissed his wife because of fornication and marries another. We recognize that both are adulterers, though the sin of one is more grave than that of the other. No one is so unreasonable to say that a man who marries a woman whose husband has dismissed her because of fornication is not an adulterer, while maintaining that a man who marries a woman dismissed without the ground of fornication is an adulterer. Both of these men are guilty of adultery" (Adulterous Marriages 1:9:9 [A.D. 419]).
"Undoubtedly the substance of the sacrament is of this bond, so that when man and woman have been joined in marriage they must continue inseparably as long as they live, nor is it allowed for one spouse to be separated from the other except for cause of fornication. For this is preserved in the case of Christ and the Church, so that, as a living one with a living one, there is no divorce, no separation forever." (Marriage and Concupiscence 1:10:11 [A.D.419]).
"In marriage, however, let the blessings of marriage be loved: offspring, fidelity, and the sacramental bond. Offspring, not so much because it may be born, but because it can be reborn; for it is born to punishment unless it be reborn to life. Fidelity, but not such as even the unbelievers have among themselves, ardent as they are for the flesh…The sacramental bond, which they lose neither through separation nor through adultery, this the spouses should guard chastely and harmoniously" (ibid., 1:17:19).