Several points need to be addressed to fully answer this question.
- What does the Hebrew actually say?
- What symbols and principles are present?
- What effect on one's longevity does the eating of blood have?
The Hebrew
The words translated as "blood" and "life" occur consecutively, with no verb between. Because the word for "life" (nephesh) has a pronominal suffix, it technically is grammatically definite. It also has a prepositional prefix which could mean "in" or "with" in this case (it is the same prefix that we find on the very first word of the Bible, usually translated as "In" the beginning...). The word for "blood," having no article attached, is non-definite.

The specific arrangement of these two words leaves some subjective possibilities for translators. Should "damow" (blood) be regarded as adjectival in usage? If considered as an attributive adjective, there should be no verb, as in: "with its life-blood." However, if considered as a predicate adjective, the linking verb is implied, as in: "with its life, [which] is the blood." Various English translations will show that scholars have differed on this, going either way in their translations.
It is true that in some contexts, "nephesh" (life) is translated as "soul." In this context, it makes better sense to render it as "life." Consider: does a "soul" have blood? We ordinarily think of the soul as something intangible, more related to one's thoughts, feelings, or character; whereas "life" is obviously connected to blood.
The Symbols
Blood, as a symbol of life, is connected Biblically with the concepts of murder (see Numbers 35); of sacrifice, with the blood of animals representing the blood of the Lamb--Jesus giving his life for us; and of unity, i.e. "And hath made of one blood all nations of men for to dwell on all the face of the earth, . . ." (Acts 17:26, KJV). To shed "innocent blood" was a crime of no small magnitude.
The root word "nephesh," meaning "life" or "soul," can be applied to souls of man as well as to animal life. It technically means "breathing creature," and, as it relates to blood, implies the oxygenation of that blood through the breath. The definition statement for a human soul comes from Genesis 2:7, where it was first pronounced by God that, having breathed into Adam the breath of life, he "became a living soul (nephesh)." Therefore, the blood which carries the breath of a creature, maintaining its life, represents that life.
Consuming Blood versus Longevity
Following the Flood, when meat was permitted to be eaten, the lifespans dropped precipitously. We may safely assume they were draining the blood as God had asked, but even then there is a residual amount that is not removed, and must be eaten when one consumes flesh foods.
Today, some studies have shown that vegetarians may outlive their meat-eating counterparts by as much as 6-13 years (there is statistically more benefit/effect for a male than for a female). Whether studies show this or not, the Biblical record honors those who were vegetarian. Consider Daniel and his three friends in Babylon.
It is interesting to note that women tend to outlive men in most every society on earth. Some believe this may be due, in part, to their regular loss of blood during their childbearing years. This eliminates excess levels of iron--an element that the body tends to conserve and, in men, has no mechanism for natural removal. Iron is an oxidizer, and tends to increase the rate of cellular aging.
Conclusions
It comes back to the core of the question: "Why can't we eat the life?" God desires us to live long and healthy lives. Blood will not keep our body in its best condition. Not only does it provide an additional source of iron--which most of us, especially men--do not need, but also it contains the body's wastes, toxins, and diseases.
If one wishes to live longer, it is quite possibly wise to do the opposite of eating blood: becoming a blood donor. Giving life to others would, ironically, extend our own. As the Bible says: "...It is more blessed to give than to receive." (Acts 20:35, KJV)