What does the phrase "that woman ought to be
killed for breaking up a home” reveal about the
society and culture?

There is a patriarchal society that values men's lives over women's basic rights.

Explanation:

Blaming a woman for a divorce (if I am correct in assuming that's what you mean by "breaking up a home") and deciding that she should be killed reveals the toxic culture in a society. It also shows that women are held to a higher standard than men, yet when they fail to meet that standard they are punished far more harshly than their male counterparts. This quote proves that violence towards women can be based upon mere beliefs or theories. Therefore, the phrase shows that women are falsely accused in this society, and it normalized by the culture.