Who knows what institutionalized children get in their schools either from the cafeteria, vending machines, teachers, and other students.
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If you took the time to visit the school you would.
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Judge them by their fruits.
Homeschoolers are fit and slim. ( I personally have never met an obese one)
The rolly-pollies waiting at the school bus stop ( like day laborers) are very likely not.
Parents choosing between institutionalizing their children or the more natural environment of the home will see the difference, if it is pointed out to them.