The Pharisees also came unto him, tempting him, and saying unto him, Is it lawful for a man to put away his wife for every cause?
Note 1 at Mt 19:3: There are many references to divorce in the Old Testament, but there is only one passage there that addresses what the grounds for divorce were - De 24:1-4. The reason a divorce was permitted was because the woman had lost favor in the sight of her husband due to some "uncleanness" found in her (De 24:1).
There were two major schools of thought in Jesus' day about what this "uncleanness" might be. The conservatives, headed by Shammai, interpreted this "uncleanness" to be fornication or adultery only. The liberals, headed by a man named Hillel, held that this could be any reason ("for every cause"), such as the way the wife combed her hair, seasoned the food, etc. Josephus, who was a first-century historian, cited De 24:1 (The Antiquities of the Jews, Book 4, Chapter 8, Section 23) and wrote that he divorced his wife because he was not pleased with her manners and behavior (The Life of Josephus, Section 76). Jesus forever settled this dispute with His answer in Mt 19:9. God only permits divorce on the grounds of fornication, and that was the "uncleanness" referred to in De 24:1.