Jesus continues on with what it means to be a "kingdom-minded" person. As He has done several times already, He addresses the cultural standard of the day: "You have heard that it was said..." Jesus again reinterprets the Jewish law for us. The phrase, "an eye for an eye and a tooth for a tooth" appears several times in the Old Testament. But this was meant to be a law (the "law of retaliation") that was imposed by civil authorities rather than individuals, in order to prevent unjust punishments. But the Jewish people of the day had used it to justify personal revenge, for which the Bible never advocates.
Remember, Jesus is not talking about governments or officials, regarding punishment of wrongdoing. In fact, the Bible is clear that they have a responsibility to do so. But in regard to individual believers, we are to love others with a neighborly love. This includes "turning the other cheek." We are to show the world that their insults will not dissuade us. As Jesus does, we are to love our enemies and those who persecute us. Romans 12:17-21 gives us a good commentary on what Jesus says in these verses.
Jesus continues: "And if anyone would sue you and take your tunic, let him have your cloak as well. And if anyone forces you to go one mile, go with him two miles. Give to the one who begs from you, and do not refuse the one who would borrow from you." Jesus is clear that His followers are to be marked by radical servitude and generosity.
What would it look like if the Church today took these words seriously? I dare say our witness in this nation would look much different. May we all have the servant-attitude of Christ toward others, even those who hate us.