This technical paper says that it's bad to restrict fats for children under two, because they'll likely become obese by the age of 20.
Low-fat intake in early life was negatively associated with body fat (particularly at the trunk site) and serum leptin concentration at 20 years, suggesting that early low-fat intake could increase the susceptibility to develop overweight and leptin resistance at later ages. These findings substantiate current recommendations against restricting fat intake in early life and open new directions for investigating the origin of obesity.
This paper describes a negative correlation of fat intake in children at 10 months and two years of age with body weight, body fat, and serum leptin at age 20. The practice of giving children a low fat diet, particularly those under the age of two, is postulated by the authors to produce epigenetic changes leading to greater degrees of adiposity in adulthood. Many governmental dietary guidelines recommend full fat milk under age two, but this is ignored by up to two-thirds of parents. Education of parents is needed to alter this pattern. In addition, these data raise the troubling question of whether current recommendations for consumption of low fat milk and other low fat foods after age two also might need additional research to determine if this association with adult overweight/obesity persists after age two. [emphasis mine]