In ancient Rome you struck a slave or lesser person with the back of your right hand to show you were superior. Striking with the palm of the right hand was only done to a social equal. The left hand was not used as it was the hand you wiped your . . . with, just like you don’t wave with your left hand in many countries today. By turning the other cheek you were demanding the person strike you again with the palm of the right hand thereby treating you as an equal. At least that’s what’s it’s believed to have meant.
Though today it means not to return aggression with aggression as you say Peter.
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