The aside in verse 11 – ‘(for under it the people received the law)’ – prepares the way for the argument of verse 12. The writer links the law itself to the same imperfect priesthood.
There is a sense in which the ceremonial law never passes away, for what it pointed to is abiding. We can still go back and study it even today; we can study its detail, but the reason we do so is to learn about Christ, not about the law itself. We can learn wonderful things from it, but the point is that now that Christ has come, we are no longer satisfied with the types and shadows. In Old Testament times, they were all that the people had and so they were of immense value. Now that we have Christ himself, we have, as it were, a new law. We worship him in a new way, in spirit and truth, and outwardly our worship is very much simplified. The detailed requirements of the ceremonial still live on, but not in their old form; now they exist in a new spiritual form: they are fulfilled in Christ and in what he has done to redeem us on Calvary.