The Greek word in the exception clause, porneia, means any illicit sexual intercourse.
I have my own theory why it is present in this exception clause which appears only in Matthew’s gospel, in Matthew 5:32 and 19:9; the parallel passages in Mark and Luke contain no exception clause.
The only other place in Matthew’s gospel where divorce is mentioned, and the key to understand the proper application of the exception clause, is Matthew 1:18-19:“Now the birth of Jesus Christ took place in this way. When his mother Mary had been betrothed to Joseph, before they came together she was found to be with child of the Holy Spirit; and her husband Joseph, being a just man and unwilling to put her to shame, resolved to divorce her quietly.”
It is my understanding that in Jewish eyes, the betrothal meant Jospeh and Mary were considered legally married but before they had “become one flesh”, i.e., before their marriage had been consumated. Since Matthew describes Joseph as"being a just man" and as having “resolved to divorce her,” it seems Matthew inserted the exception to divorce to cover Joseph’s special situation. Otherwise, how could Matthew condsider Joseph to be “a just man,” if the divorce he had resolved to obtain was contrary to God’s will as proclaimed by Jesus?
The traditional understanding of why Matthew considered divorcing Mary quietly was because learning that she had become espoused to the Holy Spirit and conceived the Messiah, he no longer had any claim on her and in his eyes believed he would be taking another man’s (God’s) wife. So, his “justness” was in realizing that Mary belonged totally to God. But, the angel told him not to fear to take Mary as his wife and also confirmed for him that her child truly was the Son of God, meaning that she would need him as her provider and protector in the world.
If I am correct in my interpretation of Matthew, this would mean a man may divorce his wife (or a woman her husband) only if, after the wedding but before the consumation of their marriage, it is discovered that his wife (or her husband) has been unchaste and already “become one flesh” with someone else.
If all this occurred before the wedding in a Christian marriage arrangement there would be no need for divorce because no marriage had taken place.
Along these same lines, it is my understanding that the Catholic Church does allow for divorce and remarriage in the case of a valid but unconsumated marriage.
No, not divorce but annulment. If a spouse decides that s/he does not want to consumate the marriage, no real marriage has taken place because the one spouse never intended to keep his/her wedding vows. However, couples may marry with the intention of never consumating the marriage by mutual consent. Such a marriage is called a Josephite marriage, named after the relationship between St. Joseph and the Blessed Virgin Mary.