Leviticus 17:11

For the life of the flesh [is] in the blood
The animal life or soulthe life and soul of every creatureand even the animal life and soul of man; agreeably to which our famous Dr. Harveywho found out the circulation of the bloodsays of itthat it is the principal part which first appears in generation; is the genital partthe fountain of life the first that livesand the last that dies; the primary seat of the soul or lifefrom whence motion and pulsation take their rise; in which the innate heat is produced the vital spirit is generated and the life consists ^F9; and therefore it is spread all over the bodyand according to the condition that it is insuch is the health and such the diseases of the body; yeathe affections of the mindsuch as fearshamejoyand anger are discovered by it. Hence Antoninus the emperormore than oncecalls the soul a vapour or exhalation arising out of the blood ^F11; and the sentiments of various Jewish writers agree herewith: says Aben Ezrait is a truththat the soul or lifewith which man livesis in the blood of the heart; so says Jarchi the soul or life depends upon the blood; and Ben Gersom observesthat the blood is the vessel of the soul to carry in it the fundamental heatand food to the parts of the body; and hence the animal only dies when the blood is removed;

and I have given it unto you to make an atonement for your souls:
that being the life of the creaturewas given for theirs to preserve them aliveand secure them from death their sins deserved; and so the Targum of Jonathan isfor the sins of the soul; which shows that these sacrifices were vicariousin the room of menand for the life of themand to atone for them; and is the reason given why blood should not be eatenat least while these typical expiatory sacrifices were used. Ben Gersom seems to intimateas if it was only the blood of those that was forbidden: his words arehence we learn says hethat they were not guilty of cutting offbut on account of the bloodwhichaccording to its way was put upon the altar; and this was the blood of the soul as it saith the blood of the bullockand the blood of the goat; but the blood that was pressed outand the blood of the members they were not guilty of cutting offon account of them:

for it [is] the blood [that] maketh an atonement for the soul;
so here was life for lifesoul for soul as Aben Ezra expresses it; it was a vicarious sacrifice and atonementtypical of the sacrifice and atonement of Christin the room and stead of his peoplethere being no atonementno remission of sins without shedding of blood; and the reason of the prohibition of eating blood was to direct to that blood as the atonement for sinand to keep up a reverence of itand a value and esteem for it; but now seeing that blood has been shed and atonement made by itthe end of the law is answeredand the reason of it ceasedand so the law itself; and as Christ's blood is now to be eaten in a spiritual sensethe eating of blood in a literal senseproperly dressedis lawful. And indeedas before observed the law concerning it was never binding upon Gentilesonly on Jews and proselytes.