There are many reasons why there are unfortunately hundreds of Christian sects and cults. One of them is poor reading skills.
Many people read various segments of the Bible out of context and apply it to themselves. That's a fatal error.
The verse you list does not apply to this day and age. It was given to Adam and Eve prior to the fall.
Before the fall, there was no need of blood sacrifice to cover our sins. After the fall, mankind was under the curse of God, and a perfect sacrifice was necessary for our salvation.
If you read the rest of the Bible, everybody ate meat. The only Christians who didn't eat meat were called weak in faith. (Romans 14:2)
The most sacred holy tradition to the Jews is Passover. The central practice is to eat a lamb. Not just eat it, but gobble it down while standing and splash the blood on the doorposts. God likes this, even though some may not understand it. It is a picture of his precious Son who's blood was spilled for us.
The priesthood was commanded to eat the meat of the animal sacrifices during the Old Testament Law.
In Acts 10, which I hope you will read, Peter is told that not only can he continue to eat meat as he had been doing, now that the church age is ushered in after Christ's ascension, he was to eat all forms of meat, even those previously considered "unclean".
Verse 13 of Acts 10 was a command from God and unmistakable: And there came a voice to him, Rise, Peter; kill, and eat.
For those on this board who aren't Christians and don't want to eat meat, that's fine, but for us Christians (as well as many other religions) meat is an essential part of our existence.
If my eating meat pleases God, then you can bet I'm going to do it. If it makes me unhealthy (which it won't if the meat is blessed by God and I make at least some attempt not to eat processed garbage), I don't care. I am promised a new body that will never get sick for eternity. The Bible teaches that the present sufferings we endure in our temporal bodies is nothing compared to the glory God's children will receive in eternity.
I know it's important to consider our current lives and health, but to do it at the neglect of the eternal is tragic.