In The Arabian Nights, how are we to understand Shahrayar's madness. Does it make sense—are male egos in male-dominated societies that frail or is this a special case?
In The Arabian Nights, or One Thousand and One Nights, Shahrayar's fury is understandable—once the Sultan realizes he can trust Scheherazade, his heart is softened by love. "Madness" is a form of insanity—on-going.
To the core of your question, this is not surprising for the culture. His is not a frail ego in the context of that culture; it is must as much a demonstration by his wife of her disrespect (in that male-dominated society) for her husband. She brings embarrassment and shame on a sultan!
In countries around the world today, a woman may be raped and it so shames the family that (unfairly and horrifically) the girl is often stoned to death because of the shame it brings to the family. In Asian cultures, we know the samurai would take his own life in a painful and horrible way when he believed he had lost his honor. These are time-honored codes. These are things we do not do in the U.S., but if we step back, too often we see countless people here have no shame—unembarrassed by their behavior. (Look at Hollywood parties, pregnancies, and marriages that last only days--or hours)—though betrayal is devastating.
We feel that punishments delivered in other countries—and specifically in this story—are uncivilized in our eyes, but many people in Western society have lost a sense of shame. Life is cheap. One asks how different are we really on some deep level.
In the story, note that the Sultan is the son of a well-loved and greatly respected Sultan in his own right.
In the chronicles of the ancient dynasty of the Sassanidae, who reigned for about four hundred years, from Persia to the borders of China, beyond the great river Ganges itself, we read the praises of one of the kings of this race, who was said to be the best monarch of his time.
Perhaps we are given this information to show that the sons are the descendants of a ancient and revered dynasty. When Sassanidae dies, he leaves his kingdom to his one son (who loves his brother so much, that he shares it with him). He is a loving man.
Schahriar's betrayal of trust is something that people in any culture can understand, but it was even more devastating for the kind, gentle and generous man Schahriar was, for the law did not dictate that he must be a kind husband:
Now the Sultan Schahriar had a wife whom he loved more than all the world, and his greatest happiness was to surround her with splendour, and to give her the finest dresses and the most beautiful jewels. It was therefore with the deepest shame and sorrow that he accidentally discovered...that she had deceived him completely, and her whole conduct [had] been so bad, that he felt himself obliged to carry out the law of the land...to put her to death.
We read of shame and sorrow that Schahriar (Shahrayar) experienced. However, it is important to note that the law of the land (we can assume in place for countless years) gives him the right to deal as society seems fit. However, it is Schahriar's fury that pushes him to repeat this punishment on all women. Scheherazade is the one who shows him that some women can be trusted.
The male egos are not frail: in some ways they are overly strong, but the same man that adores and protects his wife is shamed before his kingdom and reacts with fury, but within the limits of his society's laws. This is not a special situation. Based on what exists in countries around the world, it has been this way for many years.