Answer: First, this noble verse is a parable that Allah sets forth about the unbeliever’s mixing with the Muslim. Such association will not benefit the unbeliever so long as he has not embraced Islam; on the Day of Resurrection he will be in the Fire, and neither his companionship with nor his closeness to the Muslim—no matter how strong the friendship or the bond—will avail him, because he is not a Muslim.
As for the betrayal committed by the wife of Noah and the wife of Lot, it was a betrayal of creed, for both women were unbelievers and thus betrayed their husbands in matters of religion by refusing to enter the faith of their husbands. This counts as betrayal, but it is not a betrayal of chastity, because the beds of the prophets are protected—peace be upon them. It is impossible for a prophet to marry a woman who is unchaste, for they are divinely safeguarded from that, and likewise their households are protected.
Therefore, what is meant here by betrayal is betrayal in religion.
Some scholars have said that the betrayal consisted of the wife of Noah informing the disbelievers of Noah’s secrets and describing him as mad, while the betrayal of the wife of Lot was that she would indicate to her people the whereabouts of Lot’s guests so they could commit indecency with them.
Thus both women violated the trust that existed between them and their husbands by failing to keep secrets and by revealing what they knew of private matters and of the guests, and this is the type of betrayal that actually occurred.
In short, this was not a betrayal of honor; rather, it was either a betrayal in religion or a betrayal through divulging secrets.