Why Veganism? Moral, health, economic, religious, well-documented reasons should be enough, not to mention the increased personal qualities of tolerance, compassion, love and non-violence.
To quote Adiraja dasa "Vegetarianism, then, from the Vedic point of view, is part of something larger, the natural way of eating for those who want to make the most of their human life. In whatever way we follow, whether we become perfect spiritualists or simply purify our eating habits, we become happier and lessen the suffering in the world around us".
And God knows the world needs less suffering! This point alone should be big enough for more to "convert".