The phrase μιᾶς γυναικὸς ἄνδρα in 1 Tim 3:2 has often been misunderstood and used in inappropriate ways. The phrase literally refers to a “one-women-man.” While some have suggested polygamy as the background, this is unlikely. It is also unlikely that this refers to the requirement for an overseer to have a wife. Rather, many scholars take this as a reference to marital faithfulness, understanding this as the quality of relationships expected from those who are married.
I would like to suggest that the counterpart in 1 Tim 5:9 adds to the probability of this interpretation. In 5:9 Paul refers to ἑνὸς ἀνδρὸς γυνη, literally a “one-man-women.” In the first century women were not allowed to have multiple husbands or partners. Next, the context of chapter five is a discussion of widows (χήρα). The phrase must therefore refer to the quality of relationship experienced between the widow and her now deceased husband. To be accepted as a widow on the list, the widow must have been faithful in her marital relationship.
Thus, in 3:2, where Paul is discussing the character of leaders, it does not refer to the marital status required for those who are overseers, but rather the quality of relationship expected from those who are or were married. And thus, it refers to fidelity in marriage. This fits well with the whole section which focuses more on character qualifications than on status.
Douglas Moo acknowledges that this phrase need not exclude “unmarried men or females from the office … it would be going too far to argue that the phrase clearly excludes women….” Thomas Schreiner acknowledges, “The requirements for elders in 1 Tim 3:1–7 and Titus 1:6–9, including the statement that they are to be one-woman men, does not necessarily in and of itself preclude women from serving as elders….”
This is consistent with the argument above which notes that the most plausible explanation is to take the phrase μιᾶς γυναικὸς ἄνδρα as a reference to marital fidelity.
See further: What is the meaning of “husband of one wife” (μιᾶς γυναικὸς ἄνδρα) in 1 Timothy 3:2? and Does “One-Woman Man” in 1 Timothy 3:2 Require that All Overseers be Male?
 Although, S. M. Baugh, “Titus,” in Zondervan Illustrated Bible Backgrounds Commentary ed. C. E. Arnold (Grand Rapids: Zondervan, 2002), 3:501-2, suggests that this may be a directive prohibiting men from having concubines, and thus committing adultery, which amounts to polygamy.
 Sydney Page, “Marital Expectations of Church Leaders in the Pastoral Epistles,” JSNT 50 (1993): 105-20 and Towner 250-51 n. 42.
 Douglas J. Moo, “The Interpretation of 1 Timothy 2:11–15: A Rejoinder,” Trinity Journal 2 NS (1981): 198–222, 211.
 Thomas R. Schreiner’s “Philip Payne on Familiar Ground: A Review of Philip B. Payne, Man and Woman, One in Christ: An Exegetical and Theological Study of Paul’s Letters.” JBMW (Spring 2010): 33–46, 35.