It's my understanding that there were two schools of thought on divorce and remarriage in Christ's day. Here's what unfolded in Matthew...
Matthew 19:3 English Standard Version (ESV)
3 And Pharisees came up to him and tested him by asking, “Is it lawful to divorce one's wife for any cause?”
In Christ's day there were two schools of thought regarding divorce and remarriage. The Pharisees wanted to see if they could get Christ to pick a side in this theological debate. They wanted to know what He thought about divorce because the two most prominent schools of the Pharisees – the School of Hillel and the School of Shammai – hotly debated the issue. The debate stems from this text...
Deuteronomy 24:1 English Standard Version (ESV)
1 “When a man takes a wife and marries her, if then she finds no favor in his eyes because he has found some indecency in her, and he writes her a certificate of divorce and puts it in her hand and sends her out of his house, and she departs out of his house,
The debate arose between the two Pharisaical schools because of the ambiguity of the Hebrew word used for “some indecency”. The conservative School of Shammai took a very narrow approach to the verse. It taught that the “something indecent” refers to adultery or sexual immorality. So, by this opinion, a husband could only divorce his wife on the basis of adultery. With this understanding, the School of Shammai left little room for divorce.
The far more liberal School of Hillel interpreted the verse quite differently. They taught that “something indecent” meant just about anything that the husband found undesirable about his wife. Hillel taught that even if a wife was lacking in her abilities as a cook that that qualified as “something indecent” and was regarded as legal grounds for a divorce. We can find this debate recorded in the Mishnah:
The School of Shammai says a man should not divorce his wife unless he has found her guilty of some immoral behavior as it is written, “because he finds something indecent about her.” The School of Hillel, however, says that a man may divorce his wife even if she has merely ruined his food as it is written, “because he finds something indecent about her.” Gittin 9:10
The Pharisees wanted to know where Jesus stood on this debate. Jesus responded as follows...
Matthew 19:4-6 English Standard Version (ESV)
4 He answered, “Have you not read that he who created them from the beginning made them male and female, 5 and said, ‘Therefore a man shall leave his father and his mother and hold fast to his wife, and the two shall become one flesh’? 6 So they are no longer two but one flesh. What therefore God has joined together, let not man separate.”
Jesus uses some very powerful language here. In the KJV its translated, "cleave unto his wife". Here it is translated, "hold fast to his wife". However, the original definition of the term "cleave" means to "unbreakably adhere to", in such a fashion where as to separate the two would destroy both. This implies that a couple is in a state of being "one flesh" or "one organism". Since dividing the two would destroy both, the bond is clearly indissoluble. Jesus goes on to say, "What therefore God has joined together, let not man separate." This implies that what God has joined together, man isn't to separate, because he cannot separate... i.e. man isn't to divorce.
Of course, this was a higher standard than both schools of thought on the issue, for Jesus didn't mention any exception here. It is plain and clear. A couple is in a permanent bond that would destroy both if it were possible to dissolve.
Of course, the Pharisees respond with additional probing...
Matthew 19:7 English Standard Version (ESV)
7 They said to him, “Why then did Moses command one to give a certificate of divorce and to send her away?”
This question only makes sense if Jesus challenged the very validity of divorce itself. They honestly want to know now, if what Jesus said is true, why would Moses command the procedure of divorce? Jesus answers them as follows...
Matthew 19:8-9 English Standard Version (ESV)
8 He said to them, “Because of your hardness of heart Moses allowed you to divorce your wives, but from the beginning it was not so.
Here, Jesus tells them that Moses only commanded the procedure for divorce on account of mankind's hardness of heart, not because it was God's will for such to be so. Jesus indicates that from the beginning, from the time God created man, it wasn't God's will that a married couple ever divorce for any reason.
Then Jesus lowers the boom so to speak. Jesus clarifies his answer to them...
Matthew 19:9 English Standard Version (ESV)
9 And I say to you: whoever divorces his wife, except for sexual immorality, and marries another, commits adultery.”
Now, many will mistranslate this and basically cause it to contradict everything that Jesus just said. However, a close reading will indicate that Jesus didn't contradict Himself at all. Nor did Jesus pick either side in the divorce remarriage debate of His day. Jesus states that whoever divorces his wife, except it be for "sexual immorality" (Grk. pornea), and marries another, commits adultery." It should be noted that sexual unfaithfulness by a married person is adultery. The fact that Jesus doesn't use the term adultery here is because the pornea in question is assumedly prior to the actual wedding. This lends itself to the divorce during betrothal interpretation. To even strengthen this, read how the disciples respond to Christ's position on the matter...
Matthew 19:10 English Standard Version (ESV)
10 The disciples said to him, “If such is the case of a man with his wife, it is better not to marry.”
Please note, clearly Christ's position was one that was far more serious than what the disciples had heard from either current schools of thought. Else they wouldn't have replied with such dismay. Christ's position clearly left the disciples thinking that it would be better not to even marry if what Jesus taught was true. They felt it would be better not to marry because while Hillel and Shammai both had exceptions that applied to married couples... Jesus did not.
This is why I believe that Jesus actually defined the Law and raised the bar of holiness regarding marriage beyond what the schools of Hillel and Shammai. According to Jesus, only "indecency" that justifies divorce is one committed prior to the wedding/consummation itself. This makes sense. Because the bride was typically considered to be a virgin. If she wasn't, the entire wedding would be under false pretenses. We see the putting away of a wife in betrothal in the story of Mary and Joseph. This example provided by the actions of Joseph was what Jesus was talking about. Not a general clause allowing for divorce and remarriage based solely on sexual unfaithfulness, which flies in the face of other possible abuses and reasons that would actually be considered far worse.