Summarized by "The Council on Biblical Manhood and Womanhood," complementarianism is the viewpoint that God restricts women from serving in certain church leadership roles and instead calls women to serve in equally important, but complementary roles. Summarized by "Christians for Biblical Equality," egalitarianism is the viewpoint that there are no biblical gender-based restrictions on ministry in the church. With both positions claiming to be biblically based, it is crucially important to fully examine what exactly the Bible does say on the issue of complementarianism vs. egalitarianism.
Again, to summarize, on the one side are the egalitarians who believe there are no gender distinctions and that since we are all one in Christ, women and men are interchangeable when it comes to functional roles in leadership and in the household. The opposing view is held by those who refer to themselves as complementarians. The complementarian view believes in the essential equality of men and women as persons (i.e., as human beings created in God’s image), but complementarians hold to gender distinctions when it comes to functional roles in society, the church, and the home.
An argument in favor of complementarianism can be made from 1 Timothy 2:9-15. The verse in particular that seems to argue against the egalitarian view is 1 Timothy 2:12, which reads, “I do not permit a woman to teach or to exercise authority over a man; rather, she is to remain quiet.” Paul makes a similar argument in 1 Corinthians 14 where he writes, “The women should keep silent in the churches. For they are not permitted to speak, but should be in submission, as the Law also says” (1 Corinthians 14:34). Paul makes the argument that women are not allowed to teach and/or exercise authority over men within the church setting. Passages such as 1 Timothy 3:1-13 and Titus 1:6-9 seem to limit church leadership "offices" to men, as well.
Egalitarianism essentially makes its case based on Galatians 3:28. In that verse Paul writes, “There is neither Jew nor Greek, there is neither slave nor free, there is no male and female, for you are all one in Christ Jesus.” The egalitarian view argues that in Christ the gender distinctions that characterized fallen relationships have been removed. However, is this how Galatians 3:28 should be understood? Does the context warrant such an interpretation? It is abundantly clear that this interpretation does damage to the context of the verse. In Galatians, Paul is demonstrating the great truth of justification by faith alone and not by works (Galatians 2:16). In Galatians 3:15-29, Paul argues for justification on the differences between the law and the promise. Galatians 3:28 fits into Paul’s argument that all who are in Christ are Abraham’s offspring by faith and heirs to the promise (Galatians 3:29). The context of this passage makes it clear Paul is referring to salvation, not roles in the church. In other words, salvation is given freely to all without respect to external factors such as ethnicity, economic status, or gender. To stretch this context to also apply to gender roles in the church goes far beyond and outside of the argument Paul was making.
What is truly the crux of this argument, and what many egalitarians fail to understand, is that a difference in role does not equate to a difference in quality, importance, or value. Men and women are equally valued in God’s sight and plan. Women are not inferior to men. Rather, God assigns different roles to men and women in the church and the home because that is how He designed us to function. The truth of differentiation and equality can be seen in the functional hierarchy within the Trinity (cf. 1 Corinthians 11:3). The Son submits to the Father, and the Holy Spirit submits to the Father and the Son. This functional submission does not imply an equivalent inferiority of essence; all three Persons are equally God, but they differ in their function. Likewise, men and women are equally human beings and equally share the image of God, but they have God-ordained roles and functions that mirror the functional hierarchy within the Trinity.