@Marvin, it was only the blood and not the flesh that was seen as having the life in it. I have no idea why that is so specific, but Cofty is right. It's in Leviticus 17:14. How they rationalized eating the flesh as not part of it I don't know, that's a good question.
My remarks are not said of requirements presented in Leviticus. My remarks are said of the Noachian decree of Genesis 9. The Noachian decree prohibited eating a living animal without killing it first because it prohibited eating flesh with its life still in it, its blood. How does a person eat flesh from a living animal without eating flesh yet with its life, with its blood without killing the animal first? Blood is flesh.