If you want to promote vegetarianism among Christians, there are basically two schools of thought. (1) Some people cite the Bible, admit that Jesus wasn’t vegetarian (Luke 24:42-43), but say that vegetarianism is still a good idea because it is the original best diet for humans (Genesis 1:29), and Jesus wouldn’t like factory farming even if he ate meat. (2) Others cite historical evidence and argue that Jesus disrupted the animal sacrifice business in the temple (Matthew 21:12-13, John 2:13-16 and parallels), was vegetarian himself, and taught vegetarianism (the views of James in apostolic times, and the Ebionites thereafter).
The problem with the first view is that you undercut ethical and compassionate reasons for being vegetarian. If Jesus ate meat, then you might argue for “bigger cages,” but you couldn’t advocate vegetarianism on ethical grounds. The problem with the second view is that ethical vegetarianism is “heretical” and seems to contradict the Bible and church teachings.
Take your choice. I respect the views of my evangelical friends who take the first position, but I vote for heresy myself. It was Paul who eliminated ethical vegetarianism from Christianity (e. g. Romans 14), and most of the New Testament reflects this bias. The earliest layer of Christianity is best represented by Jewish Christianity and the Ebionites, which taught ethical vegetarianism from the beginning. “I require mercy, not sacrifice (of animals).”
The basis of the gospel is compassion for all creatures. If the heart is not open, even if you find a text that says “and verily Jesus said, ‘Go vegan,'” they will still not believe. If the heart is truly open, though, you don’t need scriptures at all.