Sorry, but I am siding with the school on this one. No child that young should be forced to be vegan.
You claim to be very careful about her nutrition and make sure she gets all the proper nutrients, but a child that young cannot get everything they need from a strict vegan diet unless you are extremely detail oriented in calculating nutritional intake from vegan diets.
All nutrients and their sources are not equal. If your child needs nutrient x from a meat source, replacing the meat with a vegan option that also has an x nutrient in it is not good enough. Meat and dairy sources of nutrients are ALWAYS superior to vegan choices because we have evolved over millions of years to get those nutrients from that source.
Different sources have different quantity, quality, and bio-availability of nutrients. If you feed your child a piece of meat with 2 grams of protein and then feed your child a vegan option with 2 grams of protein they are not going to get 4 grams of protein. These two sources will have different bio-availability and quality of nutrients. You can't simply substitute and think everything is fine. In order to make them equal your child would need to eat more quantity of food and even then the quality of said nutrients may not be the same. Young children are not known for eating the types of quantity needed to make them equal, and because you aren't there watching her you cannot guarantee she is eating the larger quantity of food she will require.
Additionally, her requirements do not stay as consistent as they do in an adult. Her requirements for nutrients are going to shift frequently, often differing from day to day or week to week based on her activities and type/quantity of growth in any given time period. You simply cannot monitor a child's nutrient requirements at a detailed enough level to guarantee she is getting the nutrients in sufficient quality and quantity on a day to day basis from a vegan diet, it just isn't possible.
You claim that your pediatrician says your kid is healthy and I believe you. From my experience with my own kids checkup they are looking at factors like height, weight, developmental milestones and then saying "yep, everything is within norm". That does not mean your child is doing fine on their vegan diet however. I strongly doubt your pedi is doing a full blood workup at every visit to check for levels of necessary nutrients. Your kid is growing and forming their brain in ways that will effect them for the rest of their lives. Just because your child seems healthy by the obvious measurements does not mean they are getting everything they need to meet the full potential of their genetics.
It seems everybody in this thread wants to argue that we shouldn't impose our choices on others and parents should be allowed to make these choices for their kids. In most matters this is absolutely correct, but there are areas where we do impose requirements on parents. We don't let parents hit their kids and we don't let parents give their children inadequate diets* (*I am not saying these are equal in severity, just pointing out in some areas we do impose requirements)
The thing is this isn't a just a cultural choice. We have evolved for millions of years to eat a certain diet. Being vegan is outside the norm of what a human has evolved to eat. I believe as an adult everybody should be able to make any choice they want when it comes to their diet and if they want to be vegan I have zero problem with it. It is much easier to be an adult and get everything you need in a vegan diet because your nutrient requirements are much lower, less complex, and much more static relatively than a growing child. As an adult you can also eat much larger quantities of food to balance out the low bio-availability and poorer quality of nutrients in a vegan diet.
As a rule I try to stay far away from imposing my beliefs on other parents. By and large, parents should be able to make whatever choices they feel are appropriate for their children. If your child wants to be vegan after they become an adult more power to them, but young children should not be vegan. Anybody with some time and google can easily see that it carries big risks and should not be encouraged.
Bring on the downvotes.