What factors led to the US government issuing nutrition guidelines in 1916?

The most important appears to be scientific discoveries related to nutrition that were being uncovered rapidly by the beginning of the twentieth century, from Chapter 2 of the Agriculture Health Bulletin No. (AIB 750) entitled "Dietary Restrictions and How They Have Changed Over Time",

When the U.S. Department of Agriculture (USDA) published its first dietary recommendations in 1894, specific vitamins and minerals had not even been discovered. Since then, researchers have identified a number of vitamins and minerals that are essential to health, and have determined the minimum levels required to prevent nutritional deficiencies such as scurvy and beriberi. Food policies such as iodine fortification of salt and the enrichment of flour products with B-vitamins together with consumer education, have eliminated many nutritional deficiencies in the United States. With the elimination of many nutritional deficiencies and improved control over infectious diseases, chronic diseases such as heart disease, cancer, and stroke have become more prevalent causes of death. Nutrition research began to focus on the connection between excessive consumption of certain dietary components fat, saturated fat, cholesterol, and sodiumand the risk for chronic health conditions. More recently, research has expanded to other dietary components such as dietary fiber and antioxidants, and the role that low consumption levels of these may play in the development of certain chronic diseases. [Davis, Saltos 1999]

The last two sentences are important as much of the success of the nutritional guidelines came from both their utility (much of which, such as the food grouping remains unchanged to today), but initially also from food industry support.

USDA publications explicitly encouraged consumers to choose foods from the full range of U.S. farm products, believing that increased consumption of U.S. agricultural products would improve the health of the general public. For nearly 35 years, the USDA received full support from the food industry when it came to the guidelines...Food industry support began to taper off in the mid-1950s to early 1960s when the focus of dietary recommendations began to shift from avoidance of nutritional deficiencies to prevention of chronic disease.

Obviously American farmers and the agricultural industry particularly liked the idea of "you need to eat all kinds of our products". When food became more plentiful after WWII and obesity more of a problem, health advice from the USDA started to change to reflect this (something that as a member of the millennial generation I find hard to understand. A government agency bucking private interest for the public good, what?).

The big motivating factor in the study of nutrition in the US was the world war, from military-nutrition.com a website maintained by the U.S. Medical Research and Material Command

The formal history of U.S. military nutrition research dates back to 1917, when the Surgeon-General’s Office established a Food Division for the purpose of “safeguarding the nutritional interests of the Army.” In the face of a possible world shortage of food during World War I, there was a need to conserve food. The U.S. Food Administration had received complaints from civilians who had observed food wastage at military training camps. In response, the Food Division instructed that nutritional surveys should be conducted to assess food requirements and economy...Military nutrition research effectively came to a stop during the years between WWI and WWII. However, the League of Nations, first established in 1919, became actively engaged in the study of nutrition after World War I (Harper, 1985).

So from what I can tell there are several motivating and interacting factors:

• Military interest in developing efficient foodstuffs for supplying a large army far away from the homeland. This extends as well to ensuring that the working population in the homeland during wartime is healthy despite food shortages.

• The economic interest of American agricultural companies and farmers many of whom stood to gain from a more diversified American diet.

• The national interest in having a healthier and more productive population that leads happier lives with less medical costs.