The Twelfth summary point of my longer explanation of the PMW says:
When the statement includes the titles “professor of theology” and “synod president” in a list of those which fall into the pastoral office, it assumes that such vocations are defined in accordance with AC articles V, XIV, and XXVIII, and the Treatise on the Power and Primacy of the Pope. That is, the duties of these vocations are primarily the administration of the external means of grace, and any distinction between them and other titles for the pastoral office is purely by human arrangement, not from God’s Word. If such a title is found to be defined in conflict with these principles, then the doctrinal statement’s categorization does not apply: it is not part of the pastoral office.
The assumption I point out here is rather important. Take the office of President, for example. Someone may say that the office of synod president must fall into the pastoral office, because the synod is a churchly organization. OK, let’s see where that takes us. We are familiar with other presidents, aren’t we? Yes, in fact every congregation has a president, usually elected in much the same way as the synod president, only by a smaller body. And isn’t a Christian congregation a churchly organization, at least as much as the synod? Of course it is. So if that’s the reason the office of synod president must be an instance of the pastoral office, then those who preside in our congregations should also be considered pastors.
The example above is only meant to show how carefully we need to consider exactly what we mean by “professor of theology” or “synod president.” What are the criteria? According to our Confessions, the pastoral office is characterized by its primary duties, which are the administration of the external means of grace.
Professors of theology may sometimes be considered to be pastors with specialized calls to teach God’s Word on Christ’s behalf, for benefit of the whole Church. That’s how Martin Luther understood his doctorate and professorship. On the other hand, we may also have people who teach theology on a different basis.
Our Confessions are especially helpful in defining what the office of synod president should entail. They state that any distinction between those who hold the pastoral office is to be considered a merely human arrangement. So if the synod president is also called primarily to administer the external means of grace, then great care must be taken not to grant him special authority over other pastors on account of his office. (We know such an arrangement well by this time, in Rome.) Beside that, I’m not sure that the synod understands the pastoral nature of its president’s duties as well as it should. More study is needed in this area, especially in light of the relatively recent shift to a full-time presidency.