Turning the other cheek was not necessarily an act of submission. Instead it may have been understood at the time to be an act of defiance against tyrrany, by standing up to it and facing it down:

"At the time of Jesus, says Wink, striking backhand a person deemed to be of lower socioeconomic class was a means of asserting authority and dominance. If the persecuted person "turned the other cheek," the discipliner was faced with a dilemma: The left hand was used for unclean purposes, so a back-hand strike on the opposite cheek would not be performed. An alternative would be a slap with the open hand as a challenge or to punch the person, but this was seen as a statement of equality. Thus, by turning the other cheek, the persecuted was demanding equality."