Why does the Torah forbid drinking blood? First of all, I should clarify that it is only arterial blood that is forbidden. What is called blood of the flesh that remains within the meat itself is not the problem. And blood from the sacrifices was sprinkled around the altar ceremonially. It was drinking the blood like wine that was forbidden.
It was common across the world as part of religious ceremonies to drink blood. In some cases, it was believed that blood gave one the strengths of the bodies it was drawn from. It was also credited with transferring brain power. Just as in cannibal societies, eating the dead enabled one to absorb their wisdom and experience. And bloodletting was supposed for a long time to be of medicinal value.
Drinking the wine in the Christian Eucharist ceremony is drinking the blood of Jesus and the wafer is his body. In literal Christianity, a miracle takes place called Transubstantiation. Miraculously, the wine actually becomes blood and the wafer flesh. In other branches of Christianity, it is symbolic.
The Torah says one should not “eat over blood” and then adds “do not pursue divination or witchcraft.” “Earing over the blood” seems to have been a pagan custom at the time of the Bible. Perhaps this was what the Eucharist was originally based on. The Torah couples eating over the blood with witchcraft and divination. Which indicates that drinking blood was associated with such forbidden practices.
Several times in the Torah in Leviticus and Deuteronomy the Torah says that “Blood is life (Nefesh).” Life blood might be a translation. It is meant to convey that blood is the source of life and therefore is something special and should be respected. Not that it should be drunk. Rather left to be absorbed into the ground and natural cycle of life.
This why it is particularly important when it comes to mundane slaughter, Hulin. The blood must be removed. If one kills animals in the wild, or birds, the blood must be covered with dust. The Temple can constrain blood within a formal structure. But outside it must be treated in such a way as to prevent it being collected or used profanely.
Not drinking blood is meant to influence us away from needlessly shedding it. Blood is linked so many times in the Torah to human life. Notably the redeemer of someone killed, the Goel HaDam who role was to see justice done. It seems clear that the repeated warnings against spilling and drinking blood are connected. It is a Torah obligation to respect life. To do whatever one can to avoid treating blood casually.
How ironic that given all the Biblical laws against drinking blood, primitive people of several religions, still believe Jews need to kill children to drink their blood for ritual purposes.