In Presbyterianism, what is the basis for a parallel between the office of deacon and Christ's priestly office? In Presbyterianism, there are three "titles" that can be given to officers of a church:


Teaching elder (e.g., pastors)
Ruling elder
Deacon


Last weekend I heard something rather novel, at least to me1—that these three titles parallel the three offices of Christ (prophet, priest, and king):


Teaching elder – Prophet – proclaims God's word
Ruling elder – King – rules and directs the church; responsible for church discipline
Deacon – Priest – ????


The parallels are obviously not perfect even in the first two cases, since ruling elders also proclaim God's word (at least in small groups and classes, if not preaching from the pulpit), and teaching elders also participate in ruling and directing the church.  Still, I can see the connection.

However, I do not see the connection between the office of deacons and Christ's priestly office.  So that's my question:

Given a Reformed and Presbyterian polity and christology, what is the basis for making a parallel between the office of deacon and Christ's priestly office?

There's likely to be some biblical basis for this, but I'm most interested in the biblical arguments made by those who hold to Reformed, Presbyterian beliefs.  Those who do not share this framework, if they make a connection between these two offices, might do so for different reasons.




This view is held by "some Reformed textbooks," according to G. I. Williamson, so it's not just the view of the person I heard it from.  Unfortunately Williamson doesn't mention which texts argue for this.
Sorry Nathaniel, I'm not able to comment yet, I'm new to this site :).
It's basically a model of Jesus's ministry and the actions of the early church. He chose several disciples/apostles, trained them in helping the poor, healing the sick, and leading the Church, and eventually set them out on their own.  See Acts 6:

Brothers and sisters, choose seven men from among you who are known to be full of the Spirit and wisdom. We will turn this responsibility over to them 4 and will give our attention to prayer and the ministry of the word.”
5 This proposal pleased the whole group. They chose Stephen, a man full of faith and of the Holy Spirit; also Philip, Procorus, Nicanor, Timon, Parmenas, and Nicolas from Antioch, a convert to Judaism. 6 They presented these men to the apostles, who prayed and laid their hands on them.
7 So the word of God spread. The number of disciples in Jerusalem increased rapidly, and a large number of priests became obedient to the faith.

Indeed, this is true in many modern Presbyterian churches. In my own, the elders typically have more longevity and lead the church intellectually and spiritually, while we've had many deacons who have been trained by our elders and pastors, given responsibilities in caring for our church members, and eventually set out as missionaries or church planters.
Hope this helps some; sorry I can't substantiate my claims more, I'm not as read-up on these topics as I used to be and as I wish I was.. In short, I believe it's a model based upon Jesus's example.