Here is my attempt at a very brief summary of the current debate/discussion surrounding the eternal functional subordination (EFS) of the Son to the Father
1. We all know the incarnate Son submits to the Father, but is His submission something that extends to His eternal role/relationship as Son? Is the Son subordinate to the Father from all eternity? Is there authority and submission within the inner life of the Trinity, even before creation and redemption?
2. Proponents of EFS say yes. Opponents say no.
3. Opponents say submission/subordination necessarily entails two wills. To have submission, you have to have one will submitting to another. But the Triune God has only one will. Now, the incarnate Christ submits to the Father because, as the God-man, He has two wills: divine and human. However, opponents of EFS maintain that having two wills in the Godhead would then require two natures (or essences, or beings) in the Godhead. And since God is one, He is one Being with one divine nature. Therefore, they say, two wills requires two natures or beings, which would separate the two Persons (Father and Son) into two gods, which is virtually Arianism. And of course, when you add the Holy Spirit to the discussion, who would then have His own will, you get a third God: tritheism.
4. Proponents of EFS question whether their position requires two wills, and/or whether two wills requires two natures. Making their case on these issues is where I think EFS proponents can bring clarity and advance the discussion. If I can understand (a) how a functional or relational subordination of the Son to the Father doesn't require two wills, or (b) be convinced that a will is a property of a person and not a nature, the EFS position would be strengthened.
5. Both proponents and opponents reject the doctrine of ontological subordination, that is, that Son is somehow inferior in His being/essence to the Father. That is Arianism.
6. However, opponents of EFS do keep arguing against proponents as if EFS necessarily implies ontological subordination. After all, they say, what would it mean for the Trinity to "function" in eternity, before they ever acted (i.e., began functioning) in creation or redemption? To speak of the Trinity in eternity is not to speak of the Trinity "functioning" or "operating" (commonly called the "economic Trinity, i.e., the Trinity working out in the economy of redemption; or the Trinity "ad extra"), but it is to speak of who God is "in Himself" (commonly called the "immanent Trinity," or the Trinity "ad intra"). If you're speaking of who God is in Himself, they say, you're speaking of His ontology, His being.
7. Proponents of EFS might reply: Whether or not "function" is the right word, there *is* an eternal distinction of *Persons* within the Trinity, and they relate to one another as Father, Son, and Spirit. Their argument is that part of what it means for Scripture to call the Father "Father" and the Son "Son" is that there is a relationship of authority and submission.
8. Opponents of EFS would say: No, fatherhood and sonship relate only to the Father's eternal generation of the Son. It is "begottenness," not authority and submission, that Scripture means to teach us when it calls the Father "Father" and the Son "Son."
9. I imagine proponents of EFS would ask why it couldn't be both, and opponents would ask why it *should* be. Proponents would respond that Scripture clearly pictures the Son as subordinate to the Father. Opponents would say that those texts refer to the Son's subordination as the God-man, in the economy of redemption, and not His eternal relationship to the Father before the economy of redemption began.
10. I'm not sure where I land yet. There needs to be continued dialog between both sides, and both sides must be fastidious in responding both (a) to what is actually said and (b) to all of what is said.
11. One thing is for sure, no matter which position you take: 1 Corinthians 11:3 teaches complementarianism. The complementarian argument isn't (or at least it shouldn't be) that since there is eternal subordination of roles within the Trinity, there ought to be subordination of roles between men and women. Rather, the argument is (or at least should be) simply this: the incarnate Son is equal in essence with the Father, yet occupies a functionally subordinate role with respect to the Father. Jesus' submission does not necessarily imply inferiority of being. In the same way, a wife is equal in essence (though not identical in essence, as is the case with Jesus and the Father) with her husband, yet occupies a functionally subordinate role with respect to her husband. A wife's submission does not necessarily imply inferiority of being.