Jesus gives three examples of what He means by not returning evil for evil. The first of these is, "If anyone strikes you on the right cheek, turn the other also." Imagine if I were your assailant and I were to strike a blow with my right fist at your face, which cheek would it land on? It would be the left. It is the wrong cheek in terms of the text we are looking at. Jesus says, "If anyone strikes you on the right cheek..." I could hit you on the right cheek if I used a left hook, but that would be impossible in Semitic society because the left hand was used only for unclean tasks. You couldn't even gesture with your left hand in public. The only way I could hit you on the right cheek would be with the back of the hand.
Now the back of the hand is not a blow intended to injure. It is a symbolic blow. It is intended to put you back where you belong. It is always from a position of power or superiority. The back of the hand was given by a master to a slave or by a husband to a wife or by a parent to a child or a Roman to a Jew in that period. What Jesus is saying is in effect, "When someone tries to humiliate you and put you down, back into your social location which is inferior to that person, and turn your other cheek."
Now in the process of turning in that direction, if you turned your head to the right, I could no longer backhand you. Your nose is now in the way. Furthermore, you can't backhand someone twice. It's like telling a joke a second time. If it doesn't work the first time, it has failed. By turning the other cheek, you are defiantly saying to the master, "I refuse to be humiliated by you any longer. I am a human being just like you. I am a child of God. You can't put me down even if you have me killed." This is clearly no way to avoid trouble. The master might have you flogged within an inch of your life, but he will never be able to assert that you have no dignity.