When Jesus speaks of the “certificate of divorce” He speaks of a man made law that by-passes God’s law. God’s original intent is overruled. So, Jesus speaks of the concept of adultery to those who break the marriage vows, either through breaking up the marriage through giving of a certificate of divorce and having the wife leave the marriage to be married again, thus causing the next man whom she marries to commit adultery, as well as “making her a victim” of adultery.
According to Jesus in the Matthew 5 passage, a man can divorce his wife for the reason of adultery. In the context of the day, we have to remember that the husband is the one who is in charge and has the right to divorce his wife if he desired. Using the Deuteronomy passage we can see that the man can divorce his wife for practically any reason; it could actually be something that displeased him. The evident purpose was, as far as possible, to favor the wife, and to protect her against an unceremonious expulsion from her home and children. Professor Driver, The German the Revised Version (British and American) (Kautzsch) Yet, the wife is not addressed here that she can do the same because the wife was close to being property according to some scholars. "In all such cases where the wife was concerned as the moving party she could only demand that her husband should divorce her. The divorce was always from first to last, in Jewish law, the husband's act." The common term used in the Bible for divorce is “shilluach” 'ishshah, "the sending away of a wife" (Deuteronomy 22:19,29). We never read of "the sending away of a husband." The feminine participle, “gerushah,” "the woman thrust out," is the term applied to a divorced woman. The masculine form is not found. Professor Israel Abrahams, Cambridge, England, before "the Divorce Commission" (London, November 21, 1910)
Even though divorce was made possible it was not necessarily easy to do. What the law tries to do is to regulate it, usually in favor of the wife. We infer from this law that a man could divorce his wife (a) only for good cause; (b) the case must be brought before some public official; and (c) a legal document prepared and placed in the wife’s hand. These formalities, involving time and money, would act as a deterrent to hasty or rash action, which end the present law would further serve. (George Arthur Buttrick, The Interpreter’s Bible Vol 2, 473-4)