Our oldest child suffered from severe stomach ailments for a time between 6 and 12 months in age. One remedy we tried was switching to skim milk for a time instead of formula (long story, but we had tried a million remedies). Our pediatrician promptly read us the riot act and explained infant nutrition to us.
What he emphasized most was the essential amino acids found only in mother's milk (or formula) and animal flesh. Without these amino acids, a child's brain does not develop fully and there is a lot of maladies that may result in other areas of the body.
Upon further research, we found that without fats from animal milk and flesh, we truely are under nourishing ourselves.
Which is not to say that it is required, to eat anywheres near the amount of meat that a typical American does.