I’ve often thought that the late Professor Kurt Marquart’s discussion of the one divine office and auxiliary offices in his book The Church: Her Fellowship, Ministry, and Governance (Confessional Lutheran Dogmatics, vol. IX, pp142f) is the most excellent explanation I’ve encountered:

[The office of school-teacher] belongs … to the “offices of parents” to see to it that their children “are educated in all piety, sciences, and arts.” Bringing up their children in the nurture and admonition of the Lord is also the parents’ obligation (Eph. 6:4), not that of pastors…. Walther [the first LCMS president] quite naturally regarded the provision of schools as a parental and civil function. “Here in America,” however, he argued, “the congregation takes the place of the government in this matter.”

How then did Walther relate the school-office to the one Gospel office? Walther held that in the apostolate Christ had “instituted only one office in the church, which embraces all others and by which the church of God should be provided for in every respect.” His 8th Thesis states therefore: “The preaching office [Predigtamt] is the highest office in the church, out of which office all other ecclesiastical office [Kirchenämter] flow.” Accordingly, “every other public office in the church is a part of [the preaching office, Predigtamt] or an auxiliary office that supports the Predigtamt, whether it be the office of those elders who do not labor in the Word and doctrine (I Tim. 5:17) or the ruling office (Rom. 12:8) or the diaconate (office of service in the narrow sense), or whatever offices…” In this context also belongs the office of schoolmaster.