If we have no idea about who the author of the book of Hebrews is, why is it included in the canon?
We do not have a detailed record of how the leaders of the early church came to consensus on what would eventually be accepted into the New Testament canon. The general impression that one gets from reading such early church fathers as Irenaeus and Origen is that the choice was made based on whether the books were considered “apostolic”. In other words, what books did the apostles themselves approve of and consider to be inspired and intended for general use by the churches. Clearly, they did not restrict the list to books written by apostles. In fact, if we include Luke, Mark and Acts in the New Testament canon (and no one questions these books), then fully one third of the New Testament is not written by an apostle. The book of Luke is “apostolic” in that it was accepted as part of the canon by the apostles and their close associates. The reason that Hebrews seems a special case, is not that it is not written by an apostle but because we are not sure of the author of the book. About its authorship, Origen stated in the early third century, “Only God knows.” Personally, I trust Origen’s knowledge on the authorship of this book better than any modern commentator because he lived so much closer to the time of writing of the book and Origen was a careful historian.
So, the fact is that we do not know the author. Why, then is it in the canon? The answer is that it is probably because it was accepted by the surviving apostles and by the other principle leaders of the very early church as inspired and deserving a place in the canon. This is my definition of “apostolic.” I would add that the book also speaks for itself as to its inspiration. If you read non-canonical books from the late first or early second century such as the Epistle of Barnabas, the Didache or the Letter of Clement of Rome, these books speak for themselves as good, but of vastly less quality. They are clearly not inspired! Read them for yourselves. I believe (but please be aware that I am speculating) that one of the reasons that Hebrews was finally accepted into the canon was simply because it is such an amazing book. We could lose Mark or Colossians from the New Testament and our Christianity would not lose all that much, but take Hebrews out of the New Testament and it would be a huge blow. I rate Hebrews as one of my four or five favorite books in all Scripture. Now that it is part of the New Testament, how could anyone look at this book and doubt its inspiration? But that is just my opinion.
Let me add one more thing, which is that I believe by faith that God oversaw what entered into the New Testament canon. As an argument for Hebrews, this would be circular reasoning, of course, but as a believer, by faith, I have confidence that God did not leave the choice of books in the New Testament to chance.