Are people short because they lacked sufficiant nutrients during childhood/puberty?
As long as a child receives a reasonable amount of nutrients, they will reach the maximum height that their genetic make-up would permit – some people are just destined to be shorter than others; no “better” foods would have made a differrence. There is, however, evidence, that a significant change in overall-population diet could cause an increase in the average height of a generation of children – witness the case with Japan in the Post-WWII eras. But even at that, the average Japanese height is not as tall as the average “westerner.” It is true that malnutrition CAN inhibit height growth – just not true that all shortness is a sign of malnutrition.