According to Catholicism and Eastern Orthodoxy, what are the strongest apologetic arguments for the divine inspiration of the deuterocanonical books?

Actually, Jordan Bajis writes in his catechetical book, “Common Ground: An Introduction to Eastern Christianity for the American Christian” (page 93) the following:



The Orthodox Church, unlike the Roman Catholic Church, only recognized 49 books as belonging to the Old Testament canon. The Eastern Church assigns a “second” place of honor after the New Testament and Old Testament cannon, to these remaining pre-New Testament book (they are referred to as deuteron-canonical books). Although these books are not valued to the same extent as other books in the Biblical canon, the East admits that they do have historical and spiritual value. These books are: Esdras I, Tobit, Judith, Wisdom of Solomon, Ecclesiasticus, Baruch, Maccabees I, II, and III, and the Epistle of Jeremiah. For further discussion see John Meyendorff, Byzantine Theology, p. 7-11.

On the other hand, in considering the spirit of the question, it is interesting to point out that while Lutherans are not bound by everything that Martin Luther writes, confessional Lutherans do unconditionally subscribe to what is called the Augsburg Confession & the Apology to the Augsburg Confession." Those confessions explicitly infer that, at least 2 Maccabees, is considered "Scripture." (Art. XXI (IX): Of the Invocation of Saints)

It's interesting to reflect that both the Greek Orthodox Church & the Lutheran Church reject the doctrine of purgatory and yet, at least the Lutherans, still considered 2 Maccabees to be Scripture. Some insight on why can be found by Lutheran theologian, Rich Futrell, here. See also his article on the Apocrypha here.

To add to what was written in the above articles, it should be pointed out that the early Lutherans did not want to dogmatically prohibit the intercession of saints. For example in the Roman Catholic contribution to “A Joint Commentary on the Augsburg Confession by Lutheran and Catholic Theologians” there is an interesting footnote on page 282. It states that according to the minutes of the discussion for the 16/17th of August:



They agree in the first place that all the saints and angels in heaven intercede for us with God. Secondly, that it is both pious and right to remember the saints and observe festivals on which we pray God to let the intercession of the saints avail for us. But whether the saints are to be invoked by us was not agreed on. Indeed, they say that they do not prohibit it, but since Scripture does not teach the invocation of the saints, they themselves do not wish to invoke them not only because Scripture does not teach it, but also because it seems to them to be a dangerous abuse. (F.W Schirrmacher, ed., Briefe und Arten zu der Geschichte des Religionsgespräches zu Marburg 1529 und des Reichstages zu Augsburg 1530 {Gotha: 1876; reprint, Amsterdam: 1968}, p. 222)

The big question is which books did Jesus put his stamp of approval upon? It appears that in the days of Jesus, Josephus writes the following:

We have but twenty-two [books] containing the history of all time, books that are justly believed in; and of these, five are the books of Moses, which comprise the law and earliest traditions from the creation of mankind down to his death. From the death of Moses to the reign of Artaxerxes, King of Persia, the successor of Xerxes, the prophets who succeeded Moses wrote the history of the events that occurred in their own time, in thirteen books. The remaining four documents comprise hymns to God and practical precepts to men. (Contra Apion 1:7-8)

On the other hand, the book of Maccabees is the single source for how a Jewish person is to celebrate Chanukah. And Brant Pitre has a nice argument for why the council of Jamnia (if it did happen), in the first century, did not decide what should be included in the canon. He points out that in the Talumdic period the canon was not settled as closed, but included the deuterocanonical books like Sirach as Scripture. So, it is conceivable that Jesus & the disciples mights have considered the deuteron-canonical books as part of their canon. See here.

As was pointed out by another responder, the Church councils at Hippo (393) and Carthage (397, 419) listed the deuterocanonical books (and the other 66 books) as Scripture. While it could be that the councils were in error, the Lutheran church (in their confessions) has given it the benefit of the doubt that the councils were in touch with an apostolic oral tradition of what Jesus used for the canon of his day.

And that would be the strongest Roman Catholic argument as well. The Holy Spirit worked on in the early church to bring them into an agreement on what was faithful to the apostolic witness related to what should constitutes the canonical Scriptures.