Vegetarian children?

At lunch at the aforementioned Kingdom of Vegetarians yesterday, the conversation turned to the question of when a child’s wish to convert to vegetarianism for ethical reasons should be indulged by his or her parents (the primary conversants were not vegetarians and were facing this dilemma with children of varying ages). For my own somewhat obscure reasons, I’m interested in gathering more data on people’s views on this issue, so if you feel like indulging my curiosity, give me your answer and, if you feel moved to do so, your reasoning in this thread.