Hebrews 9:13, 18, 26

Under the old covenant the blood of bulls, goats, and the ashes of a heifer were sprinkled on those who were defiled and effectively cleansed them outwardly from their ceremonial impurities.

So this is why not even the first covenant was inaugurated without the blood of animals.

for that would mean he must suffer repeatedly ever since the fall of the world. But now he has appeared at the fulfillment of the ages to abolish sin once and for all by the sacrifice of himself!