It seems that this arrangement is being made because divorce is already regularly happening. Possibly it has even been practiced in Egypt. The purpose of this prescript seems to be to discourage a loose divorce. If someone has sent his wife out of his house and she is married again and is then send away again, then the first man is not allowed to take her back as his wife.
Although God, because of the hardness of their hearts, has allowed them to send their wives away, He considers the next marriage of the woman to be defiled. Therefore the Lord Jesus says that anyone who marries a woman who is send away by her husband commits adultery. This could not be so if God were to recognize divorce as a lawful thing. But for God there can be no legitimate reason for divorce.
There is no explicit consent to divorce anywhere. It is permitted, because of the hardness of heart (Mt 19:88He *said to them, “Because of your hardness of heart Moses permitted you to divorce your wives; but from the beginning it has not been this way.). God hates divorce (Mal 2:1616For I hate divorce,” says the LORD, the God of Israel, “and him who covers his garment with wrong,” says the LORD of hosts. “So take heed to your spirit, that you do not deal treacherously.”). This arrangement is also made to prevent a man from always acting according to will, at his discretion. He could change women as often as he likes. What a confusion that would cause in family life. Finally, there would also be no clarity about the inheritance.
The reason for sending away can be anything the man describes as “some indecency”. In any case, it has nothing to do with adultery, because therefore death penalty applies (Deu 22:20-2220“But if this charge is true, that the girl was not found a virgin,21then they shall bring out the girl to the doorway of her father’s house, and the men of her city shall stone her to death because she has committed an act of folly in Israel by playing the harlot in her father’s house; thus you shall purge the evil from among you.22“If a man is found lying with a married woman, then both of them shall die, the man who lay with the woman, and the woman; thus you shall purge the evil from Israel.). If he sends the wife away, he must give a certificate of divorce. She then has proof that her first husband renounces her and is no longer allowed to take her to wife.
God has given Israel a certificate of divorce: “And I saw that for all the adulteries of faithless Israel, I had sent her away and given her a writ of divorce” (Jer 3:8a8And I saw that for all the adulteries of faithless Israel, I had sent her away and given her a writ of divorce, yet her treacherous sister Judah did not fear; but she went and was a harlot also.). How long did God not hesitate before He gave that letter? Finally, God had to write the certificate of divorce, because it is an apostate people who, as it is, will never return to blessing. For the people as a whole there is no recovery. What is being restored is a remnant of the election of grace (Rom 11:5,23-245In the same way then, there has also come to be at the present time a remnant according to [God’s] gracious choice.23And they also, if they do not continue in their unbelief, will be grafted in, for God is able to graft them in again.24For if you were cut off from what is by nature a wild olive tree, and were grafted contrary to nature into a cultivated olive tree, how much more will these who are the natural [branches] be grafted into their own olive tree?). Grace goes beyond the law. In this remnant God accepts His people again, while they as a whole have been whoring away from Him.
For the church as nominal Christianity, the moment of the certificate of divorce also comes. No restoration is possible for this Christianity either (Rev 18:2121Then a strong angel took up a stone like a great millstone and threw it into the sea, saying, “So will Babylon, the great city, be thrown down with violence, and will not be found any longer.; Rom 11:21-2221for if God did not spare the natural branches, He will not spare you, either.22Behold then the kindness and severity of God; to those who fell, severity, but to you, God’s kindness, if you continue in His kindness; otherwise you also will be cut off.). However, in the present time there is still a Philadelphia (Rev 3:7-137“And to the angel of the church in Philadelphia write: He who is holy, who is true, who has the key of David, who opens and no one will shut, and who shuts and no one opens, says this:8‘I know your deeds. Behold, I have put before you an open door which no one can shut, because you have a little power, and have kept My word, and have not denied My name.9Behold, I will cause [those] of the synagogue of Satan, who say that they are Jews and are not, but lie—I will make them come and bow down at your feet, and [make them] know that I have loved you.10Because you have kept the word of My perseverance, I also will keep you from the hour of testing, that [hour] which is about to come upon the whole world, to test those who dwell on the earth.11I am coming quickly; hold fast what you have, so that no one will take your crown.12He who overcomes, I will make him a pillar in the temple of My God, and he will not go out from it anymore; and I will write on him the name of My God, and the name of the city of My God, the new Jerusalem, which comes down out of heaven from My God, and My new name.13He who has an ear, let him hear what the Spirit says to the churches.’). This is indicated in verse 55“When a man takes a new wife, he shall not go out with the army nor be charged with any duty; he shall be free at home one year and shall give happiness to his wife whom he has taken..