Complementarianism, as the name implies, is the position that men and women complement each other. Both sexes are equal but different.
Egalitarianism, again like the name implies, is the position that man and women are equal. Both sexes are equal, full stop.
Already in these (very) basic definitions you can see the main issue is how can men and women be different to each other if both sides agree they are equal. In what sense or to what degree do these positions differ? Step back a bit and ask yourself before reading further: "Is there any difference between the sexes?"
I think this can be answered in both the affirmative and the negative.
Yes of cause there is a difference between genders. Listen to almost any stand up comedy routine and you will see this fact exaggerated. Males and females have different anatomy, have different strengths, biological chemical make ups and some would say they even show their emotions differently.
But both male and females make up humanity, and despite these mostly biological difference mentioned above, their humanity unites them together. In today's culture you would be hard pressed to find someone that says women are not equal to men in respect to their value as a person. It may be pointed out there is an inequality between the sexes (say in pay or representation in some career), but this inequality can be seen as unjust and something to rectify because men are equal to women and vice versa.
In both these negative and positive senses there is no debate between the complementarian and the egalitarian. The division between the complementarian position and the egalitarian position is over the topic of gender roles. So again, ask yourself: "Is there any difference between what a man and a woman can do?" Again, this can be answered with both a yes and a no.
Woman can not compete in the 4x100 men's freestyle in the Olympics. That is not discrimination. If men and women competed together in some sports it would be deemed unfair as women and men have different strengths and weakness. Look at gymnastics for example. Gymnasts don't even compete on the same apparatus as their opposite gender. But, when it comes to the sport of shooting, it is beyond me why they separate the males and the females. I'm sure an Olympic women can shoot as good as any Olympic man. In the equestrian males and females compete against each other, and that I think is fair.
But what about examples away from the biological limitations that each sex has? Can a woman or a man be a CEO of a successful company? What about leading a band or an empire, or be Governor General or Prime Minister of this great country? And of cause the answer is yes. Yes women can have all those jobs. Again the complementarian and the egalitarian do not differ on these points. (The position that says women can not lead in society might be the position of patriarchy).
The real difference comes not from talking about gender roles in general, but when talking about specific roles in the church and in the (Christian) home. Why these two aspects? Because that is what the Bible talks about. So that is where the lines are drawn. It is not about some general job or position out there somewhere, but specifically in roles within the church and the (Christian) home.
The opponents to egalitarianism sometimes say that the egalitarianism project their secular view of equality into the Church whereas the complementarian just sits on what the Bible says (and the patriarchal position projects their Church views into the secular world). This might be a bit strong as there are lots of verses in the Bible that argue for equality, but the important point is to see in what sense the sexes are equal. Hopefully we will look at these. (Feel free to throw some verses in the comments below that you want me to look at).
Both sides affirm everyone is equal in value and worth because of the Imago Dei but the complementarian will go further and say this doesn't necessarily mean our roles are exactly the same within the Church or within family life. It takes lots of different jobs for society to function well, and although some jobs may (incorrectly sometimes) be esteemed better than others, the person doing the undervalued job is still considered equal in worth and value like any other person who is doing a so called "better" job.
So far we haven't looked at a single Bible verse, so take this post or leave it. The following posts in this series will be closely looking at all sorts of texts supporting the equality of both sexes, but also the differences in role both sexes have in regards to Church and family life.