It's been my entirely anecdotal experience that almost every person who is vegetarian or vegan is so not because they correctly applied any sort of reason or logic or even studied food to any great extent, but because they have religious beliefs along the lines of "Meat is murder." These people, having abandoned reason and logic -- or worse, abused it to support their religious beliefs, are almost impossible to get through to.
Something similar is true of socialists. They have religious beliefs like "The poor should be helped" and "Workers should control production." But these people didn't always abandon reason and logic, or intentionally abuse it. Most of them have merely been brainwashed and misled, in crude violent government indoctrination centers at that, and getting through to them is not nearly as difficult. Simply show the truth: that government doesn't and can't help people, only hurt them.