Probably the same thing Blessed Augustine or +Athanasius the Great or +John Chrysostomos were doing when they used the same example for the same reason.
BTW, Corinth, far, far away from Rome, maybe as far as 3-4 days’ sailing from Italy, was within his jurisdiction, Constantinople not having been established at that point. Had he written to Christians at, say, Alexandria or Antioch making the same arguments, that might mean something. But so far as we know, he didn’t.
But if the 12 Apostles are prefugured in the 12 tribes of Israel, and the bishops are heirs of the Apostles, then which bishop holds the rod of Aaron?
Oh, the irony.