Problem: Peter writes, “In the same way, you wives, be submissive to your own husbands” (1 Pet. 3:1). Elsewhere, Paul writes, “The man is the head of a woman” (1 Cor. 11:3), and he states, “Wives, be subject to your own husbands” (Eph. 5:22). Is this a sexist attitude toward women? Critics argue that this is ancient patriarchy at its worst.
Solution: In order to understand this passage, we need to consider its context. Peter opens this statement by writing: “In the same way…” This refers back to 2:13, where he writes, “Submit yourselves for the Lord’s sake to every human institution.” Therefore, Peter is expounding upon how to live in a hostile world under fallen human institutions. Marriage was instituted by God (Gen. 2:24), but our exercise and experience of marriage is always in a fallen state in a fallen world. Peter is demonstrating how to live in a godly way in a fallen marriage, and he commands that wives should submit to their husbands in order to win their husbands over to Christ.
In a similar way, Peter explains that believers should submit to unjust government (2:13-14) and the unjust institution of slavery (2:18-20). Of course, the NT authors do not condone unjust governments or slavery. However, Peter is commanding these Christians to submit to these unjust institutions in view of Christ’s submission for us (2:21-25) and for the purpose of avoiding further persecution (2:15).
In this passage (3:1), Peter is continuing on in this theme. He is telling Christian women to submit to their unbelieving husbands (“disobedient to the word”), so that they can win them to Christ (“they may be won without a word by the behavior of their wives”). In other words, the purpose of Peter’s teaching needs to be taken in view of evangelism.
This interpretation particularly comes into focus, when we consider the historical backdrop of Greco-Roman society. In this culture, women were forced to stay at home with their husbands, and they wouldn’t have friends of their own. Scholar Karen Jobes explains the historical background:
In Greco-Roman society it was expected that the wife would have no friends of her own and would worship the gods of her husband (Plutarch, Advice §19)… The very fact that a woman would adopt any religion other than her husband’s violated the Greco-Roman ideal of an orderly home (Oborn 1939: 133)… The husband and society would perceive the wife’s worship of Jesus Christ as rebellion, especially if she worshipped Christ exclusively… The wife’s attendance at Christian worship would provide the opportunity for her to have fellowship with other Christians who possibly were not her husband’s friends.
For this reason, Peter tells these women to submit to their husbands, so that they could win them over to Christ. Without winning them over, they would have no way of getting out of the house at all! This also explains why Peter tells these women to refrain from wearing makeup and fancy clothing, when they were leaving the house (3:3-4). If a Christian woman was dressing up to go to her Bible study, this would look suspicious to the unbelieving husband.
Peter’s imperative for submission is primarily for evangelism, but Paul also mentions submission for the purpose of God’s design (Eph. 5:22; 1 Cor. 11:3; Col. 3:18).
 Karen H. Jobes, 1 Peter, Baker Exegetical Commentary on the New Testament (Grand Rapids, MI: Baker Academic, 2005), 203.