74 Accordingly, as our Lord ordained what the apostle declares Him to have ordained,— namely, that those who preach the gospel should live of the gospel,— He gave these counsels to the apostles in order that they might be without the care of providing or of carrying with them things necessary for this life, whether great or the very smallest; consequently He introduced this term, “neither a staff,” with the view of showing that, on the part of those who were faithful to Him, all things were due to His ministers, who themselves, too, required nothing superfluous.
And thus, when He added the words, “For the workman is worthy of his meat,” He indicated quite clearly, and made it thoroughly plain, how and for what reason it was that He spoke all these things. It is this kind of power, therefore, that the Lord denoted under the term “staff,” when He said that they should “take nothing” for their journey, save a staff only. For the sentence might also have been briefly expressed in this way: “Take with you none of the necessaries of life, neither a staff, save a staff only.”
So that the phrase “neither a staff” may be taken to be equivalent to “not even the smallest things;” while the addition, “save a staff only,” may be understood to mean that, in virtue of that power which they received from the Lord, and which was signified by the name “staff” [or, “rod”], even those things which were not carried with them would not be wanting to them. Our Lord therefore used both phrases. But inasmuch as one and the same evangelist has not recorded them both, the writer who has told us that the rod, as introduced in the one sense, was to be taken, is supposed to be in antagonism to him who has told us that the rod, as occurring again in the other sense, was not to be taken. After this explanation of the matter, however, no such supposition ought to be entertained.
Source: The Harmony of the Gospels (New Advent)