Jesus refutes the teaching that a man is “required” to dispense with his wife when he suspects unfaithfulness. Jesus finds such behavior intolerable, saying Moses did not “command” men to divorce wives; he “permitted” it because of the hardness of people’s hearts (see Mk 10:5). The springboard for right action should not be hard-heartedness, but love. Jesus says that only if a woman has done something that irreparably ruptures the marriage can such a divorce be right. But it isn’t a necessary response.
This passage can be read as follows: “Whoever does the following commits adultery: divorces his wife (except for immorality) and remarries another.” Judgment is placed on the person who remarries after pursuing an illegitimate divorce. If the divorce is invalid, so is the remarriage. But the reverse is also true: If the divorce is valid, then remarriage is acceptable.