Of course, food is often a touchy subject even in non-vegetarian homes. My desire to eat nothing but plain chicken and bagels throughout my childhood caused plenty of bitter fights, and contributed to my parents' early fear that my vegetarianism was just another form of pickiness. In retrospect, I'm not sure why I hated all foods with flavor so much, but I do know that kids start searching at a relatively young age for ways to exercise their own autonomy, and food choice is one of these ways. So should the children of vegetarians get to choose to eat meat?
Emily Sohn of the LA Times addresses several issues surrounding this question, including health. It's a common misconception that growing kids need meat to survive. I remember a sort of legend that made the rounds in college about a student who tried to raise her toddler vegan; all the kid's teeth fell out, and had to be replaced with metal ones. The metal is, I think, a dead giveaway that this story was bullshit (although I'd kind of like to get a look at little Johnny Steelfangs), but it's true that vegetarian and especially vegan diets for kids require a few tweaks. As Sohn says, small children may need calorie-rich foods like peanut butter because a vegetarian diet can otherwise fill them up without giving them enough energy. And breastfeeding vegan moms may need a B12 supplement. But horror stories aside, a meat-free diet shouldn't do kids physical harm.
Then there's the psychological angle. As Sohn points out, "school-age children in particular can become anxious when anything about them is different from their peers, including what they eat for lunch." This actually seems like an opportunity for educating kids about differences — after all, children are always going to stick out in some way, and if parents can teach them to stand up for what's in their lunchboxes, they may be better at standing up for what's in their heads.
What seems more difficult to negotiate is a kid's desire to separate herself from her parents — including their dietary restrictions. Of course, many parents exercise some control over what their kids eat, and in some religions, dietary rules have been passed down for millennia. But, as Sohn notes, "resentment can build up if foods are forbidden completely." And at some point, kids are going to have the opportunity to try a hamburger. Parents can tell their children why they believe vegetarianism is important, and they can make only vegetarian foods at home. But when it comes to the big, bad, omnivorous world, probably the best they can do is teach them to make informed choices and not to let anyone else think for them — including mom and dad.