Whatever the rational, "blood sacrifices" were obviously very important in the beginning of every early culture. See A deeper, more historical explanation may be the most primitive of realizations.
Some considered a gift of blood as necessary to carry one's petitions to god/dess.
The ancient word bleodswean and the Old English word bletsain (blessing) meant to sanctify by application of blood. Sprinkling the blood of the sacrificed on the people was once the acceptable way to bless them. This sprinkling motion is still used in many Christian churches to bless. The Bible passage "His blood be upon us, and our children" (Matthew 27:25) is actually an acceptance of the Blessing of the Holy Sacrifice of Jesus' Blood - not an acceptance of guilt and blame by the Jews (nor should the passage be used to blame anyone if not one's self for the need of redemption by the blood of the perfect lamb).
Many alters today are blessed with salt (a universal substitute for blood).
The Satapatha Brahmana says that "In the beginning the sacrifice most acceptable to the gods was man." Then substituted for humans were, in order:
The transition from humans to animals was not steady or smooth. Sometimes both would be sacrificed, or humans only annually. If life became particularly difficult, say most of one's volcanic island was blown way by an eruption and there wasn't much food or hope left, human sacrifice would sometimes return.
The transition continued as a piece of parchment (real sheep's skin) replaced the animal. Writing on the parchment and burning it was sufficient to carry a partition to god/dess.
Nowadays, Writing one's desires on a piece of paper and placing it beneath a burning candle does the trick.
As societies changed, killing one's first born became distasteful, and rituals were substituted for the actual killing of the infant.One such ritual is infant circumcision (the Hebrews adopted the Egyptian male adolescence rite [indicating the male to be as powerful/valuable as the female because he could bleed, also] and Moses moved it to infancy so his son would not need to be totally sacrificed). Animal sacrifices were still required.
The success of rituals that required the burning of the sacrifice often depended on a large amount of smoke rising to show the acceptance of the sacrifice by god/dess.