As in much of Jesus' teaching, pressing his illustration the wrong way may obscure his point. In fact, this would read Scripture the very way he was warning against: if someone hits us in the nose, or has already struck us on both cheeks, are we finally free to hit back? Jesus gives us a radical example so we will avoid retaliation, not so we will explore the limits of his example (see Tannehill 1975:73). A backhanded blow to the right cheek did not imply shattered teeth (tooth for tooth was a separate statement); it was an insult, the severest public affront to a person's dignity (Lam 3:30; Jeremias 1963:28 and 1971:239). God's prophets sometimes suffered such ill-treatment (1 Kings 22:24; Is 50:6). Yet though this was more an affront to honor, a challenge, than a physical injury, ancient societies typically provided legal recourse for this offense within the lex talionis regulations (Pritchard 1955:163, 175; see also Gaius Inst. 3.220).
In the case of an offense to our personal dignity, Jesus not only warns us not to avenge our honor by retaliating but suggests that we indulge the offender further. By freely offering our other cheek, we show that those who are secure in their status before God do not value human honor. Indeed, in some sense we practice resistance by showing our contempt for the value of our insulter's (and perhaps the onlookers') opinions! Because we value God's honor rather than our own (Mt 5:16; 6:1-18), because our very lives become forfeit to us when we begin to follow Jesus Christ (16:24-27), we have no honor of our own to lose. In this way we testify to those who insult us of a higher allegiance of which they should take notice.
I appreciate Henry's perspective on this, and I believe he is right. While there are certain instances where it is right to "stand up for yourself," ultimately the demand to keep your own honor and dignity in the sight of men is a futile trap. And human honor is not only of little value in comparison to our status before and fellowship with God, but there is a sense in which we mock the system of the world in our refusal to play by its rules. We stand outside it, in judgment over it, just as Jesus did. Far from showing surrender, it shows that we operate on a different plane and have the courage to remain there.