The writer now turns back from the illustration of a will to the main subject, which is the covenant. That is why is a possible translation of the Greek, but this verse does not in fact draw a logical conclusion from verses 11-17. The link between verses 16-17 and 18 is the play on different senses of the word for will or covenant. This play on words is made possible by the fact that blood or “death” was involved in both. Jerusalem Bible has “the earlier covenant needed something to be killed in order to take effect.” A comparison or analogy, not a proof, is involved. Therefore some more general translation, such as “So,” “In this way” (Die Bibel im heutigen Deutsch and Traduction œcuménique de la Bible), “Hence” (Revised Standard Version, Moffatt, New American Bible), or “Thus,” may be more appropriate than That is why or “It was for this very reason” (Barclay).
The Greek word used for went into effect is not a legal term. It is most often used in the Bible in speaking of the dedication or inauguration of the Temple; in 10.20 it means “to open a path.” Here and in verse 19 the writer is concerned with the ceremonies which took place when the first covenant came into effect. The Greek is different for reasons of style, but the meaning is close to the term translated goes into effect in verse 17, with the added suggestion of a ceremony. Die Bibel im heutigen Deutsch has simply “So the first covenant became valid only through blood.”
The concept of went into effect or “was inaugurated” is sometimes expressed idiomatically; for example, “was cut,” “was made to stand,” “was tied,” or “bound the persons.”
As in verse 7, Good News Translation simplifies the double negative, meaning “not without blood,” into only with the use of blood, which is more usual in common language. With the use of blood may be expressed as “by means of blood” or “by means of death.”
Quoted with permission from Ellingworth, Paul and Nida, Eugene A. A Handbook on The Letter of the Hebrews. (UBS Handbook Series). New York: UBS, 1983. For this and other handbooks for translators see here .