My friend, I am a faithful Catholic. I don’t “question its Catholic nature.” I believe that the Church was founded by Jesus. I was indeed reading the Didache, and I was previously aware of its powerful presentation of the Eucharist thanks to reading excerpts from it. I have no other opinion about any non-Catholic society that may have produced it. You’ve misunderstood my purpose in asking the question.
I spend a lot of time around very smart and knowledgeable Protestants, mostly evangelicals and Pentecostals, who have their own mental picture of the Early Church. It looks very different from the Catholic picture. Catholics read something like the Didache, note its translation of the early Eucharistic prayer, and say, “See? Catholic!” (Indeed, I find that section of the Didache very moving.) Pentecostals, on the other hand, are far more likely to note its extensive prescriptions for the treatment of prophets (almost as long as the section on the Eucharist), and say, “See? Pentecostal!” They will point to the fact that eucharisteia means “thanksgiving,” and indeed that even Catholic translations of the New Testament never once translate eucharisteia as “Eucharist” but always as “thanksgiving.” They will argue that there’s no good evidence that the writers of the Didache had the same understanding of the Eucharist that the Catholic Church does, and that translating eucharisteia as “Eucharist” rather than “thanksgiving” in this case was a poor translation choice. (I’m a translator by trade, and in general it’s not a bad argument to question whether a translator was truly aware of cultural context. Translators make weird mistakes all the time, even when translating from one modern language to another. Again, I am a Catholic, not someone hostile to the Catholic faith. I don’t know enough about the cultural context of the Didache to judge whether this would be a worthy argument in this case–I simply know enough about the craft of translation to know that translations are always questioned.)
To give another example, I’ve cited 1 Co 11:29 to a group of home churchers, imagining, again, that this was a slam-dunk “proof-text” for Catholic Eucharistic theology. Nope, they’ve heard it, they take it very seriously, but they believe it has to do with the Corinthians being greedy and taking too much of the “love-feast” food (they seem to be thinking of this as something like a weekly potluck dinner) without being conscious of the needs of the poor… and that’s why people were sick and dying, because they were starving. They accused me of taking the verse out of context!
So, when I read texts that are cited as evidence for the Early Church being the Catholic Church, I intentionally read them with a very critical, Protestant-type eye, looking for items that would suit the confirmation biases of my Protestant friends. Sometimes when I do this, I come up with a criticism that stumps me, and that’s when I turn to Catholic Answers. Mintaka’s perspective on my question was very helpful.