A while back, in a comment, the question was asked “Was the Didache inspired by God.”
Obviously it was never (to my knowledge) included in canonical scripture, but appears as a book commended nonetheless by Athanasius (Ep. fest. 39.7) and known to Eusebius who is slightly less complimentary (Hist. eccl. 3.25.4–6a), whereas Rufinus states (if he is referring to the entire Didache and not simply the two-ways chapters, or even to the κ document incorporated into Apostolic Church Order) that the book is not canonical whilst it is ecclesiastical (Symb. Apost. 38). In other words the only “canon lists” which refer to the Didache do so in order to exclude it.
But what, in any event, does the questioner mean by “inspired by God”? Direct verbal inspiration? Here we meet the problem of presupposition. I would struggle, for instance, to suggest that (say) the narratives of the Gospels are inspired in that sense, although would admit that the prophetic speeches of the Johannine Jesus (deriving, I suspect, from the activity of prophets in the Johannine Christ-group) are inspired directly. I might class, for instance, the Didache’s instructions for prayer, baptism, and eucharistic meals as, like the narratives of the Gospels, the work of authors or redactors who were faithful to their tasks and were simply concerned to present the truth about God as they knew and understood it. And I cannot exclude the possibility that they were assisted by the Holy Spirit in doing so. Such is the catholic understanding of “inspired by God”, but such a definition might be extended to a great deal that is not, nor was ever considered to be, canonical scripture.
I am finally inspired(!) to answer the question, over two years after it was posed, through coming across Amiel Drimbe, “The Didache – Between Canons and Canonicity” Plērōma 21 (2019), 105-147.
Abstract: Modern scholars identify six major criteria that the early Church employed to determine the canonicity of NT writings: apostolicity, orthodoxy, antiquity, use, adaptability, and inspiration. It could be that, at some point, the Didache satisfied most, if not all criteria. In this study, however, I have argued that the Didache was never considered for canonicity on a larger scale. This was due to its original design and evolving nature. Namely, it was meant to be a companion writing, and it was a living text. Thus, the Didache was a writing for the canons, but not a canonical one.
I think this is a very helpful way of looking at the question. What I realized in reading Drimbe’s article is that the Didache refers back to the Gospel, whether that be a written or an oral Gospel. It thus explicitly states its own secondary nature. Not only does it not claim to be inspired, it implicitly denies any such inspiration; as such, for all its antiquity, claimed apostolicity, recognized orthodoxy, and utility, it is not canonical, nor was ever considered such, and never claimed inspiration.