See this question about divorce explained in the notes at Matthew 19:1-12.
And if a woman shall put away her husband - It would seem, from this, that a woman, among the Jews, had the power of separating herself from her husband, yet this right is not given her by the law of Moses. There is not, however, any positive evidence that females often claimed or exercised this right. Cases had occurred, indeed, in which it had been done. The wife of Herod had rejected her former husband and married Herod. And though instances of this kind “might” have been attempted to be defended by the example of Pagans, yet our Saviour was desirous of showing them that it did not free them from the charge of adultery. The apostles were going forth to teach Pagan nations, and it was proper for Christ to teach them how to act in such cases, and to show them that they were cases of real adultery.