This is a great article with science and anecdotes in the NYT about how much of the "nutrition education" for children can be so dangerous. A 4 or 6 year old is not cognitively developed enough to learn about nutrition the way we think about it. Their job should be deciding how much, not what to eat. Its why I'm so scared with the push for nutrition education in preschools and daycare. Labeling foods as "good" or "bad," "healthy" or "unhealthy" (which a child will just turn into good or bad) makes judgements about food and brings guilt, fear, and shame into the relationship with food.
Chances are your school staff are not trained to provide appropriate nutrition education. Many argue they shouldn't be doing it at all, while they should be providing positive food experiences perhaps through cooking, tasting, or garden experiments linked to science class- all presented without judgement. You may want to look into what messages your kids are getting from their educators. Though well-intentioned, the message may not be benign.
Variety and moderation are the key to good nutrition.