Please read this more detailed discussion of divorce as taught by Jesus in the Sermon on the Mount in Matthew 5:31-32:
In Jesus’ day, confusion prevailed about the grounds for divorce. Even the rabbis could not agree on what constituted the “uncleanness” of Deut 24:1. Followers of Rabbi Shammai felt adultery was the only grounds for divorce. Those who followed Rabbi Hillel accepted many reasons, including such things as poor cooking.
The gospels record four statements by Jesus concerning divorce. In two of these He allowed divorce in the case of adultery. In Matt 5:32 Jesus commented on the situation of both the woman and her new husband: “Whoever divorces his wife for any reason except sexual immorality causes her to commit adultery; and whoever marries a woman who is divorced commits adultery.”
In another statement, Jesus described the position of the man who divorced his wife: “Whoever divorces his wife except for sexual immorality, and marries another, commits adultery; and whoever marries her who is divorced commits adultery” (Matt 19:9). While these two statements seem to allow divorce because of unfaithfulness, two other statements of Jesus appear to make no provision for divorce (Mark 10:11-12; Luke 16:18).
Are Jesus’ statements allowing divorce for infidelity in conflict with biblical statements that seem to forbid it entirely? Jesus’ statements in Mark and Luke were made in conversations with Pharisees about the Mosaic Law, which they believed allowed divorce on grounds other than adultery (Deut 24:1-4). Jesus’ main point in these statements was that divorce is contrary to God’s plan for marriage and should never be taken lightly. Even though Moses allowed divorce, this was an exception granted under the law because of their “hardness” of heart (Mark 10:5). Jesus desired to put “teeth” into the Law by declaring that, even if the divorced couple had not been sexually unfaithful to each other, they would commit adultery in God’s sight if they now married other partners.
In allowing divorce for the single reason of “immorality,” or illicit sexual intercourse, Jesus’ thought is clearly that a person dissolves his marriage by creating a sexual union with someone other than the marriage partner. Such union violates the sacred “oneness” intended by God when he united Adam and Eve in the first marriage relationship (Gen 2:18-25).
In the case of sexual unfaithfulness, the decree of divorce simply reflects the fact that the marriage has already been broken. A man divorcing his wife for this cause does not “make her an adulteress,” for she already is one. Thus, divorce on the grounds of unchastity usually frees the innocent partner to remarry without incurring the guilt of adultery (Matt 19:9). However, this is sometimes questioned. Although Jesus allowed divorce for adultery, He did not require it. On the contrary, He insisted that divorce disrupts God’s plan for marriage and left the way open for repentance and forgiveness.
Paul was essentially in agreement with Jesus’ teachings on marriage and divorce. However, the apostle dealt with new situations involving the marital conflict between believers and between a believer and a non-believer.
In the case of two Christians Paul admonished them to follow the Lord’s teachings and be reconciled. In any event, neither is to marry another (1 Cor 7:10-11). In 1 Cor 7:15, Paul says that a Christian whose mate has abandoned the marriage should be free to formalize the divorce: “If the unbeliever departs, let him depart, a brother or a sister is not under bondage in such cases.” Many authorities hold that the phrase “not under bondage” means that a deserted Christian spouse may lawfully go from divorce to remarriage. But other scholars disagree with this interpretation. In any event, Paul encourages the believer to keep the marriage together in hopes that the unbelieving partner might be saved (1 Cor 7:16).
(from Nelson’s Illustrated Bible Dictionary, Copyright © 1986, Thomas Nelson Publishers)