Or maybe that document was only dealing with teachings/practices that were in dispute at the time. Remember that not every historical document was intended as an exhaustive treatise. Some of the most valuable ancient documents are those that were dashed off quickly, because they give us a snapshot of the mindset of the time.
The Didache was apparently written as a very basic introduction to proper practices (not beliefs) of the Christian community.
To state in a 1st-century document (knowing that they had the writings of Paul, then Peter, then the Gospels and the catholic epistles) that Jesus is God the Son or that the Eucharist is the real presence of Christ would have seemed like “Captain Obvious”.
In fact, most 1st-century christian writings, especially the NT epistles, were written to correct specific errors and heal specific schisms within the Church, and not as a catechism or a statement of what the entire church faithful already believed. Those beliefs, as St. Paul cited, were first delivered to the saints orally by the apostles and their successors. Remember, at that time and throughout most of history, most people were illiterate and could only receive the gospel as taught to them orally by representatives of the Church. It wasn’t until the 1800’s that literacy was common in the West. It is still not common in much of the developing world.
If you want debates about the defections and schisms in the early church, read the Early Church Fathers. They wrote in great detail about the conflicts, small apostasies and rebellions and some really wicked sins involving the early church (yep, warts and all). I like “The Faith of the Early Fathers” by Jurgens in 3 volumes. There are many others that go into more or less detail. There is a good one called “The Fathers Know Best” that many people find helpful.
I think that that is what makes Christian history (and all history) so much fun. We try to put ourselves in the ancient authors’ shoes, or moccasins or boots, learn about the way they lived and then try to figure out why they were writing what they wrote.
Paul (formerly LDS, now happily Catholic)
P.S.: I am currently fascinated by a series of historical books on ancient America, before and after Columbus. They are “1491”, “1492” and “1493” by Charles C. Mann. These are some of the best books I have ever read.