Complimentarianism and Egalitarianism are the topic of debate most between Christians, although some parts of the Lost, Outside world may debate the concept.
For the record, Complimentarianism is a system of thought--or view if you prefer--that believes that God has created men and women with specific roles to play in this world that equally bring glory to Him, are equally valuable and necessary, and that fit together in such a way that manhood and womanhood work together perfectly to reveal the bests in each other and achieve things in the best way, which is God's way--id est, men and women compliment each other in God's eternal design.
Conversely, Egalitarianism is a system of thought--or view--that believe that God has created men and women equal, that it is only because of the fall that there is any seeming inequality (although in truth, Complimentarians would agree to this, they would explain it differently), that in Christ now there are no difference in equality in terms of ethnicity, social status, and gender (something Complimentarians would also agree to, but not mean the same as Egalitarians), thus they believe that anyone, man or woman is eligible for leadership offices in the church (pastors/elders/bishops/etc.) and outside thereof as well (civic, professional, etc.) if qualified.
Both of these views have their own spectrum on which their adherent may fall. Both sides have many thing they agree on as well. Both try to base their views off Scripture, usually at least, although there are always some who swing by personal bias rather than the Spirit and God's Word. The main differences between these two views are their applications of Scripture and their emphases in Scripture. At the end of the day, this is a disagreement of views of person hood and what equality means. The main rub for Egalitarians is that they believe that to allow only one of the genders to hold spiritual leadership offices in the Church is unjust--that it is unequal treatment. They have a problem with restricting people from what they desire to do--people should be free to attain whatever status they desire. Similarly, they tend to focus on free will and are found main among those who espouse a high focus on it. Also, they often are be low-church in orientation. Further, many of them are in the Arminian camp theologically. For example, the Assemblies of God are Egalitarian and fit the aforementioned description.
In contrast, the Complimentarian view takes issue with the concept that everyone must have the same opportunities to be equal. Moreover, the rub comes with the concept of erasing the concept of gender that God create as good. Their focus is on the teleology of the person--that is what that person was created for--thus, they take issue with Egalitarianism in terms infringing God's intentions. They think that in fact it demeans men and women to say that there is no real difference between them and ignores that God is the God of Order and Everything-with-a-Purpose. Likewise, Complimentarians tend to come from Calvinistic or semi-Calvinistic circles. Often they are affiliated with more high-church orientations. They therefore focus on the Sovereignty and Glory of God. The fundamentally believe that people should be what God wills them and creates them to be.
Honestly, both sides have their own sets of abuses and extremes. Egalitarians would let unqualified people into offices, for example--id est, they will let just anyone be whatever they want regardless. Complimentarians can allow those in spiritual offices to abuse their power and subject women especially to mistreatment. God definitely abhors both extremes.
Now to the point, I am very much a Complimentarian and for a variety of good reasons. However, often Egalitarians cite Galatians 3:28 as proof of equality meaning everyone can be what they want in Christ, for in Christ there is no difference between Jews and Greeks, Slaves and Freemen, and Males and Females. Thus, I am left to wonder whether Complimentarianism really is the view of God. However, I am now convinced that Galatians 3:28 is not support for Egalitarianism whatsoever. The following is an exegetical interpretation of Galatians 3:28 that I believe to be true, which does not allow this to support Egalitarianism, and perhaps even supports Complimentarianism. I will admit however that I could be in error, but as far as the Spirit has so far led, I believe the following to be the true interpretation of the truth of God's Word. I will give you the context of the passage and then continue on to the specifics of the verse. So without further ado...
"But now that faith has come, we are no longer under a tutor. For you are all sons of God through faith in Christ Jesus. For all of you who were baptized into Christ have clothed yourselves with Christ. There is neither Jew nor Greek, there is neither slave nor free man, there is neither male nor female; for you are all one in Christ Jesus. And if you belong to Christ, then you are Abraham's descendants, heirs according to promise. Now I say, as long as the heir is a child, he does not differ at all from a slave although he is owner of everything, but he is under guardians and managers until the date set by the father. So also we, while we were children, were held in bondage under the elemental things of the world. But when the fullness of the time came, God sent forth His Son, born of a woman, born under the Law, so that He might redeem those who were under the Law, that we might receive the adoption as sons. Because you are sons, God has sent forth the Spirit of His Son into our hearts, crying, "Abba! Father!" Therefore you are no longer a slave, but a son; and if a son, then an heir through God."
--Galatians 3:25-4:7
Now, for Galatians 3:28, in Greek
οὐκ ἔνι Ἰουδαῖος οὐδὲ Ἕλλην οὐκ ἔνι δοῦλος οὐδὲ ἐλεύθερος οὐκ ἔνι ἄρσεν καὶ θῆλυ πάντες γὰρ ὑμεῖς εἷς ἐστε ἐν Χριστῷ Ἰησοῦ
--here is my transliteration for those unable to read that:
'ouk 'eni 'Ioudaios 'oude `Ellen 'ouk 'eni doulos 'oude 'eleutheros 'ouk 'eni 'arsen kai thelu pantes gar `umeis `eis 'este 'en Christo 'Iesou
--here is my translation of the Greek
"There's not (or "not is in") a Jew nor a Greek; there's not (not is in) a slave nor a freeman; there's not (not is in) a male and a female, for you all are one in Christ Jesus"
The key, I think, to the whole debate for this verse is a)Context, and b) Paul's weird change up of rhythm and terms when discussing the last "there's not" phrase. Firstly, as to the Context. there are some things to note. One, the context is talking about salvation by faith alone. Two, the context is talking about being heirs to the Promise given to Abraham by being sons of God and Abraham in Christ Jesus. Three, the verse taken alone (although a foolish thing to do) is focusing on unity, not equality. Four, the context mentions wrapping oneself in Christ in terms of heirship and sonship (this will be important once I explain).
Secondly, Paul changes from his not-nor trend to a not-and trend. This is odd. It clearly puts emphasis on the Male-Female section. Also, due to nature of how language is used and what the change means. With regard to Jew-Greek and Slave-Freeman, Paul writes: "NOT a Jew and NOT a Greek" and "NOT a Slave and NOT a Freeman". This means that there is not either of them. Both do not exist. They are moot. gone, nil. However, when Paul gets to Male-Female, he writes: "NOT a Male AND a Female". This can mean 5 things in the language:
1) it can mean that there is not Male-Female (i.e. male and female would be considered one concept, not two concepts, so it is not there is not male and female as two separate concepts, but rather there is not male-female as one concept);
2) it can mean that there is not both of them separately (however, this is not likely to my knowledge as a translation and very not likely given the context of the change from not-nor to not-and--the focus is on the AND);
3) it can mean that there is not a male, EVEN female (this might be possible grammatically, but very unlikely and it does not make sense as far as reading--I don't consider this an option);
4) it can mean that there is not both male and female, but that there is only female, for although the NOT means that you cannot have both of them together, you could have one all by itself, in this case female (however, this does not fit very well with context, which is talking about sons);
5) it can mean that there is not both male and female, but that there is only male, for you cannot have each one, but you could have one, in this case the male (given the context, the male makes the most sense, rather than the female, because of all the talk of sons and heirs).
The Question to ask is "Which option is right?". Connected to that, we should ask, "Why would Paul change the pattern and theme of not-nor?" This is where the context comes in. We need to ask this question of Galatians 3:28: "What question is this verse answering?" Firstly, I say the fifth option is right, because of the answers to the next to questions. Paul, I believe, changed the pattern to put emphasis on one simple fact, in Christ we are all heirs, and if heirs, sons. In fact, the whole point of this verse is to emphasize the importance of us all being sons in Christ Jesus. Being in Christ Jesus is a key theme for Paul throughout many of his letters--it is a position of ontological fellowship with Christ Jesus by the Father's Grace through faith and in the Spirit. It is our salvation, our position of salvation. The point is that we are sons and heirs in Christ Jesus. Above all that is what we are in Christ Jesus, we are not Jews and not Greeks, not Slaves and not Freemen, and not male and female--we are just males, sons, heirs in Christ Jesus. Only males, sons, could be heirs. Remember this is in the context of salvation by grace alone, so when it comes to salvation, we are only male--that is we are only eligible for being an heir, a son. In terms of salvation, we are equal, we are heirs and sons. We are wrapped up with Christ Jesus the Son, we are not female when it comes to salvation, we are heirs to the Promise, we are sons. So then, what question is this verse answering, "Who are we in terms of salvation in Christ Jesus?" The answer is twofold: We are not Jews, Greeks, Slaves, Freemen, we are male heirs and sons of the Promise in Christ Jesus, for we are one in Christ Jesus. We are united and share the position of heirs and sons in Christ Jesus by God's grace through faith in the Spirit!
On a side note, I have translated all the adjectives of Galatians 3:28 substantively, that is to say as nouns for that is the best way given the context and the grammar. Male ('arsen) seems to come from the word for "lift up/take/take away"--'aipo. Female (thelus) comes from the word for "give the breast/suckle" (thelazo), which comes from the word for nipple (thele). Also, male and female are both adjectives, but are used twice in Scripture (Matt. 19:4 and Mark 10:6) to quote from Genesis how God created them. This could denote that gender is meaning to be thrown out, but I disagree because of the context. Therefore, the contexts denotes that there is a special role and position for sons that of receiving the Promise down from Abraham (and the curse through Adam) and leadership. Therefore, this verse, besides clearly not supporting the aims of Egalitarianism, may actually support the view of Complimentatianism.
Please do let me know what you think. Feel free to critique and criticize. Interact. We want the truth after all. Ask questions and I will try to answer as well. Thanks.