Augustine of Hippo, on Heb 8:3

They do not understand that not even the proudest of spirits could themselves rejoice in the honor of sacrifices unless a true sacrifice was due to the one true God in whose place they desire to be worshiped. This sacrifice cannot be rightly offered except by a holy and righteous priest, and it also must be received by those for whom it is offered. And it also has to be without fault, so that it may be offered for cleansing those with faults. This is at least what everyone does who wants a sacrifice to be offered for themselves to God. Who then is so righteous and holy a priest as the only Son of God who had no need to purge his own sins by sacrifice, neither original sins nor those that are added by human life? And what could human beings more appropriately choose to be offered for themselves than human flesh? And what could be more fitting for this immolation than mortal flesh? And what could be cleaner for cleansing the faults of mortals than the flesh born in and from the womb of a virgin without any infection of carnal desires? And what could be more acceptably offered and taken than that the flesh of our sacrifice be the body of our priest? And so, where four things are to be considered in every sacrifice—(1) to whom it is offered, (2) by whom it is offered, (3) what is offered, (4) for whom it is offered—the same one and true mediator himself, reconciling us to God by the sacrifice of peace, might remain one with him [the Father] to whom he offered, might make those one in himself for whom he offered, and he himself might be in one both the offerer and the offering.