The disagreement between them was not about the question whether divorce as such is allowed. Both assumed that it was. They differed only about the question whether the “indecency” (Deuteronomy 24:1) in the woman must consist of issues that publicly (in the view of a third party) are considered indecent and unacceptable or if they also consist of matters that are an issue only internally (indoors) and that (more subjectively) are indecent and unbearable for the man in question. The second point, we may add, gives more possibilities for divorce (Shammai) but thereby in fact intends to limit the number of them because the woman will try the harder, also indoors, to prevent being sent away, by showing love and care for her husband, also privately.1
2 And Pharisees came up and in order to test him asked, “Is it lawful for a man to divorce his wife?”