Thank you for asking.
The main reason that we shouldn't eat animals is because of the horrible pain and suffering that is inflicted upon virtually all farmed animals.
God may have allowed the concession to eat flesh because of the hardness of the human heart, but it was never His creation (Genesis 1:29-31) or heavenly intent.
And, nowhere in the Bible are humans granted permission to cause animals to suffer, particularly as happens on factory farms which supply over 95% of all animal products.
To see what we are talking about, please take a look at our Animal exploitation section: http://www.all-creatures.org/anex
In the Love of the Lord,
Frank and Mary