The ordeal of the Sotah.
If a man’s wife is surprised (in flagrante delicto) with another man, both shall be tied and thrown into the water, but the husband may pardon his wife and the king his slaves.
Rabbi Roy Tanenbaum, paraphrased.
There is no such thing as magic; trial by ordeal does not work. We know that, the Rabbis know that, the Torah knows that. So what is the ritual of the sotah all about? When the ritual is allowed to proceed to the end, the woman will always be found innocent. It is about establishing that the woman is innocent (whether or not she is), thus restoring trust between the partners and allowing the marriage to continue.
Rabbi Claude Vecht-Wolf, https://www.sefaria.org/sheets/179349.1
In the 2nd Commandment, God has established that only He must be worshipped. Only His presence is allowed in our lives - not any other gods
Yet, here, where the marriage is collapsing, He is demanding that his name be destroyed, at the expense of saving the marriage - if the marriage has reached the stage where either the woman did commit adultery or the man suspected she had - both parties have removed the spirit Godliness from their Union.
God's investment in the marriage is such, that He is willing to have His name erased - to save the union of these two people - and both the husband and wife know what is at stake, if they reach this point in their marriage - the destruction of God's name.
God is surely acting as the ultimate Marriage Counsellor!
Rabbi Harold Kushner, Etz Hayim Humash, page 796
We can understand the promise of v. 28, that if the woman is found innocent, she will be able to "retain seed", as foreseeing that she will be restored to a life of love with her husband. But even if the ordeal and a subsequent pregnancy turn the husband's heart back to his wife, what will it take to restore her trust in him and affection for him?
Ruth Calderon, from notes to the story "Sisters" in A Bride for One Night.
The biblical ritual of the Sotah was later tempered by the sages. They sought to abolish the ritual in an attempt to replace dramatic divine intervention with pragmatic human solutions. The sages encouraged the couple to separate by means of a financial agreement, with as little hoopla as possible. The site of judgment was thus shifted from the temple to the courtroom. Moreover, in an effort to limit the practical application of the ritual, the sages created an intermediate stage in which the husband is required to state explicitly, in the presence of two witnesses, the identity of the man whom he suspects. As a result, many women were saved from death and from the force of their husbands’ jealousy, and more important to the sages, the community was thus spared unnecessary upheavals and disturbances of the peace.
The sages, experts at communal leadership, were averse to supernatural intervention. They preferred tranquility to truth, and they formulated principles that forged a new atmosphere in which jealousy was less rampant. These principles include: “Most sexual acts are attributed to the husband.” In other words, children of uncertain paternity are assumed to belong to the husband. In addition, they declared, “The man who raises the child, and not the man who conceives it, is considered the father.” That is to say, fatherhood is constituted by the act of child rearing rather than procreation.
Thus the enlightened force of leadership won over more primitive ritual. Did this indeed improve the situation of women? It is hard to tell. As this story suggests, a woman suspected of adultery in the rabbinic period could find herself divorced with a child in her womb, abandoned and penniless without even a dramatic story to share.
Prof. Hanna Liss. https://www.thetorah.com/article/the-sotah-ritual-permitting-a-jealous-husband-to-remain-with-his-wife
5:15 (then) the man shall bring his wife to the priest….
Verses 12b–13a state the facts of the case: A woman (repeatedly) cheated on her husband. He—and this is important—knows about it, or at least believes that he does. If he didn’t, there wouldn’t be any ordeal. However, she was not caught in flagrante delicto (v. 13aβ), as this would call for a death sentence. Instead, she is brought to the priests and will be subject to the ordeal.
. . . the case is not suspected cheating, with the jealousy merely explaining why the husband is bringing the case. Rather the case is that the husband suspects cheating and he is feeling jealous. The priests need to deal with the jealousy as much as they need to deal with the accusation.
Ruaḥ qinʿa, the “spirit of jealousy” that comes over the man, expresses this state of being: A man believes his wife has committed adultery, he still wishes to remain with her, but fears the consequences of such a decision. Thus, he turns to the ritual not as a way of uncovering her infidelity but of proving her innocence. More specifically, the ritual removes the prohibition, which I believe already existed in the biblical period, of his remaining married to a woman who was ostensibly unfaithful to him. . . .
Therefore, torat haq-qena’ot, the “law of the jealousies,” does not provide a means to convict a woman of adultery . . . but a means of reuniting the couple.