The writer to the Hebrews wants to make clear that the way Jesus has engaged the sacrificial system, the system that had always managed the community’s sin, was such that he changed things forever. Rather than offering the blood of an animal, Jesus allows himself to become the blood sacrifice of the people.
But this materially challenges the whole system. Jesus’ blamelessness was such, that there was no justifiable reason that could be upheld for his lynching. The fact that he was killed served to show up the motives of those who perpetrated this cruel and violent crime.
Yet in doing so, Jesus also offers an entirely alternate way of dealing with sin. Rather than blaming (and killing) others, take responsibility and repent. Rather than obey the instinct for self-interest… follow the one who gives himself.