There are two primary viewpoints on the question of whether women can serve as elders in the church. The egalitarian view holds that women can serve as elders as long as they fulfill the requirements as outlined in 1 Timothy 3:1-7 and Titus 1:5-9. The complementarian view affirms the opposite and states that women are not allowed to serve in the capacity of elder within the church of Jesus Christ.
Let’s look at 1 Timothy 3:1-7: "The saying is trustworthy: If anyone aspires to the office of overseer, he desires a noble task. Therefore an overseer must be above reproach, the husband of one wife, sober-minded, self-controlled, respectable, hospitable, able to teach, not a drunkard, not violent but gentle, not quarrelsome, not a lover of money. He must manage his own household well, with all dignity keeping his children submissive, for if someone does not know how to manage his own household, how will he care for God’s church? He must not be a recent convert, or he may become puffed up with conceit and fall into the condemnation of the devil. Moreover, he must be well thought of by outsiders, so that he may not fall into disgrace, into a snare of the devil." (ESV)
The first thing to notice in this passage is the number of masculine pronouns (“he” and “his”). The pronouns "he," "his," and "him" occur 10 times in 1 Timothy 3:1-7. As a result, just a cursory reading of this passage would lead the average person to conclude that the role of an elder/overseer must be filled by a man. The phrase “husband of one wife” also indicates that the office of elder is assumed/intended to be fulfilled by men. The same points are also made in the parallel passage of Titus 1:5-9.
The passages that describe the qualifications and duties of elders/overseers do not open the door for women to serve as elders. In fact, the consistent use of male pronouns and terminology argues strongly for the office of elder/overseer being restricted to men only. As with other issues in this debate, the question of women serving as elders is not a matter of chauvinism. In no sense is this a matter of men being superior to women. Rather, God restricts the office of elder to men only because that is how He has structured the church to function. Godly men are to serve as leadership, with women serving in the crucially important supporting roles.