Many biblical scholars have noted that Jesus' teaching radically challenged Jewish marriage and divorce customs. This article details several ways in which the status quo is overturned. For reference, here are the two passages on which the following comments are based.

Matt 527  “You have heard that it was said, ‘Do not commit adultery.’ 28 But I say to you that whoever looks at a woman to desire her has already committed adultery with her in his heart..."

Matt 193  Then some Pharisees came to him in order to test him. They asked, “Is it lawful to divorce a wife for 'any cause'?” He answered, “Have you not read that from the beginning the Creator made them male and femaleand said, ‘For this reason a man will leave his father and mother and will be united with his wife, and the two will become one flesh’?  So they are no longer two, but one flesh. Therefore what God has joined together, let no one separate.”

They said to him, “Why then did Moses command us to give a certificate of dismissal and to divorce her?” Jesus said to them, “Moses permitted you to divorce your wives because of your hard hearts, but from the beginning it was not this way. Now I say to you that whoever divorces his wife, except for immorality, and marries another commits adultery.”

10 The disciples said to him, “If this is the case of a husband with a wife, it is better not to marry!” 11 He said to them, “Not everyone can accept this statement, except those to whom it has been given. 12 For there are some eunuchs who were that way from birth, and some who were made eunuchs by others, and some who became eunuchs for the sake of the kingdom of heaven. The one who is able to accept this should accept it.”

We may note at least five areas in which he departed from the teaching of the Pharisees:

    1. Monogamy reflects the will of God, not polygamy. Although polygamy was becoming rare in the 1st century, it wasn't illegal (even if it was more expensive to maintain two wives).
    2. Lust is the equivalent of adultery (even if only hyperbolically). The point isn't that lust wasn't recognized in Judaism as sinful and dangerous (Job 31:1; Prov 5-7), but that since Jewish men were permitted to take another wife, there was no requirement of unique sexual loyalty towards one's wife. Sexual acts with a woman other than one's first wife were not an offense against that wife. Adultery was considered as a crime against a husband: one man sleeps with another man's wife (a sort of "property" crime), or a man's wife sleeps with another man.
    3. Divorcing for "any cause" (essentially the first-century equivalent of today's "no-fault divorce" was unacceptable. There had to be legitimate grounds, or else the divorce was invalid. Since such "any cause" divorces were so common, Jesus was in effect stating that the vast majority of divorces and remarriages were adulterous.
    4. Forgiveness for adultery: Whereas Jewish society (including religious leaders) insisted that a man divorce an adulterous wife, Jesus reminds his hearers that divorce is permissible only in cases of hardheartedness. That is, when the unfaithful partner refuses to repent. Otherwise things are to be worked out in the marriage. Our reaction is not to be quitting the marriage, but the path of grace, forgiveness, and perseverance. (Admittedly, this is not always possible.)
    5. Permanent singleness is a spiritually legitimate choice. In a world where marriage and offspring (esp. sons) were highly valued, there was tremendous pressure to marry, and on women to bear children. But Jesus rejects these traditional values, announcing that marriage isn't for everyone. Even today few churches honor Jesus' teaching, adopting instead to worldly norms of family and sexuality—and even mocking or teasing those who are still unmarried. As far as we know, Jesus never married—a highly unusual  decision for a rabbi.

No wonder Jesus Christ was such a controversial figure during his lifetime—and has been ever since!