An animal's blood is viewed as the essence of its life, as we find in the English expression "life's blood". The blood exemplifies the beast's animation as well as its bestiality. Human beings too have animal energy and a bestial nature; but the Torah urges us to distinguish ourselves from the beasts and give expression to our uniquely human nature, the expression of our Divine image.
When we pour out the blood of sacrifices on the base of the altar, it is as if we pour out our bestiality. This is an atonement for our souls, which sin by occasionally yielding to their lower, bestial impulses. Only then do we offer up the rest of the sacrifice. We do have the ability and responsibility to elevate and sanctify some aspects of the material, but not the lowest and basest aspects, which must be demonstratively discarded.
If on the contrary we eat the blood, it is as if we are anxious to assimilate the bestial nature of the animal to our own natures. Indeed, pagans drank animal blood for this very reason - they believed that drinking the blood, the essence of the bestiality, would bestow some of the animal's savage energy on the blood-thirsty celebrant. (See Rambam's "Guide to the Perplexed" III:46. This practice is also mentioned in Homer.)
For this reason we are extremely scrupulous about eating blood. We do not limit ourselves to pouring out the "life-blood" which exudes naturally following slaughter, but we also thoroughly salt the meat in order to extract the blood which is normally absorbed in the meat. (SA YD 69.)
RINSING THE MEAT
Halakha demands rinsing the meat before salting as well as after salting. This order is very important, and the meat can be ruined if it is salted before rinsing.
The halakhic reason for this is that while salt has the ability to extract the absorbed blood, it also has the property of pickling, which is like cooking. Salting the meat before rinsing off the surface blood could pickle this blood into the meat, rendering it forbidden (SA YD 69:2).
We could compare the surface blood and absorbed blood to our outer flaws, deficiencies in thoughtful behavior, and our inner flaws, deficiencies in character. We should first strive to repair our public flaws, corresponding to the rinsing, and only afterwards work on more subtle imperfections, through a searing character analysis corresponding to the salting. Hypocritically reversing this order shows disdain for derekh eretz, and risks making our behavior even more difficult to rectify.
Exposing our hidden flaws is not enough; once they are out in the open we have to rid ourselves of them - corresponding to the final rinsing.
Some organs can not be koshered merely by salting and rinsing; they require special treatment. Perhaps we can discern a certain symbolism in these rules.
The heart can be salted only after it is torn. This is because the blood is so strongly absorbed in this organ. (SA YD 72.) Rav Amnon Bazak has related this to the role of the heart as the seat of our emotions. In order to purify our deepest feelings, a wrenching emotional experience may be necessary. This reminds us of the famous epigram of Rav Menachem Mendel of Kotzk, "There is nothing more complete than a broken heart".
The liver is so full of blood that salting is not enough eliminate it. It is koshered only through roasting. (SA YD 73.) The liver is considered the seat of anger. (See Berakhot 61b; Shemot Rabba on Shemot 7:14.) While all character traits can be rid of their negative tendencies and used for good, anger is perhaps the most difficult of all to purify. This is hinted at in the difficulty of ridding the liver of its blood.