Problem with our modern translations is they really do a poor job of conveying what the originals actually meant. The language of the time. Idioms.
Self-defense?
The backdrop to this teaching is that the Jews considered it an insult to be hit in the face, much in the same way that we would interpret someone spitting in our face. Bible scholar R. C. Sproul comments: "What's interesting in the expression is that Jesus specifically mentions the right side of the face [Matthew 5:39]....If I hit you on your right cheek, the most normal way would be if I did it with the back of my right hand....To the best of our knowledge of the Hebrew language, that expression is a Jewish idiom that describes an insult, similar to the way challenges to duels in the days of King Arthur were made by a backhand slap to the right cheek of your opponent."
Prior to His crucifixion, Jesus revealed to His disciples the future hostility they would face and encouraged them to sell their outer garments in order to buy a sword (Luke 22:36-38; cf. 2 Corinthians 11:26-27). Here the "sword" (Greek: maxairan) is a dagger or short sword that belonged to the Jewish traveler's equipment as protection against robbers and wild animals. A plain reading of the passage indicates that Jesus approved of self-defense.
Self-defense may actually result in one of the greatest examples of human love. Christ Himself said, "Greater love has no one than this, that he lay down his life for his friends" (John 15:14). When protecting one's family or neighbor, a Christian is unselfishly risking his or her life for the sake of others.
Theologians J. P. Moreland and Norman Geisler say that "to permit murder when one could have prevented it is morally wrong. To allow a rape when one could have hindered it is an evil. To watch an act of cruelty to children without trying to intervene is morally inexcusable. In brief, not resisting evil is an evil of omission, and an evil of omission can be just as evil as an evil of commission. Any man who refuses to protect his wife and children against a violent intruder fails them morally."
While I agree with the last paragraph and to see a child hurt without doing something is unthinkable, I think defending the lives of others is not the same as preserving your own or another's at the cost of anothers. That's like valuing only your brothers' lives, but not your enemies' lives.
'Love your enemies, do good to those who curse you, pray for those who mistreat you'.
The same way, if being slapped on my own face is a jewish insult, then to turn the other cheek for someone to slap the other side, is to say 'do as you want with me because I offer no retribution'.
'For vengeance is God's'
The same way, to lay down your life for a brother, is not the same as to take a life for your brother. If we only value or love those close to us, then we're no better than anyone who doesn't know holiness. 'For don't even the pagans do that?'
Jesus says 'put away your sword, for those who live by the sword, die by the sword', and heals the ear of the guard who was struck, then proceeds to let the Jews take him, incarcerate him, brutalize him and crucify him for the sakes of the same people who are doing it. Jesus healed one of the men who was involved in his capture, and by proxy his execution, and rebuked his own brother for striking. What more can be said than that, as a statement of non-violence towards enemies?
Jesus says 'there is no greater love than this, that a man give up his life for others'. When he said this, he wasn't talking about 'fighting those' and 'killing those' in order to 'save these', he was talking about his own style of sacrifice. Giving himself up willingly and without violence, IN PLACE of another, that he might save them. The 'others' he talks about in this sentence are 'the world'. Jesus willing GAVE his life up. To GIVE one's life up is to offer no resistance. This statement is Jesus reassuring the disciples, 'I love you more than you can know'.
Finally, the statement 'sell your coverings that you may buy yourself a sword', read the lines before and after. It would make no sense that Jesus would advocate the violence considering what he says afterward. Jesus himself has said that he has a 'two-edged sword', however it isn't a literal one. It becomes self evident as you read.
Then Jesus asked them, “When I sent you out without purse, bag or sandals, did you lack anything?”“Nothing,” they answered.He said to them, “But now if you have a purse, take it, and also a bag; and if you don’t have a sword, sell your cloak and buy one. It is written: ‘And he was numbered with the transgressors’; and I tell you that this must be fulfilled in me. Yes, what is written about me is reaching its fulfillment.”The disciples said, “See, Lord, here are two swords.”“That’s enough!” he replied.Jesus went out as usual to the Mount of Olives, and his disciples followed him. On reaching the place, he said to them,“Pray that you will not fall into temptation.” He withdrew about a stone’s throw beyond them, knelt down and prayed, “Father, if you are willing, take this cup from me; yet not my will, but yours be done.” An angel from heaven appeared to him and strengthened him. And being in anguish, he prayed more earnestly, and his sweat was like drops of blood falling to the ground.When he rose from prayer and went back to the disciples, he found them asleep, exhausted from sorrow. “Why are you sleeping?” he asked them. “Get up and pray so that you will not fall into temptation.”While he was still speaking a crowd came up, and the man who was called Judas, one of the Twelve, was leading them. He approached Jesus to kiss him, but Jesus asked him, “Judas, are you betraying the Son of Man with a kiss?”When Jesus’ followers saw what was going to happen, they said, “Lord, should we strike with our swords?” And one of them struck the servant of the high priest, cutting off his right ear.But Jesus answered, “No more of this!” And he touched the man’s ear and healed him.Then Jesus said to the chief priests, the officers of the temple guard, and the elders, who had come for him, “Am I leading a rebellion, that you have come with swords and clubs? Every day I was with you in the temple courts, and you did not lay a hand on me. But this is your hour—when darkness reigns.”