There were a number of arguments made in favor of US expansion and imperialism in the late 19th and early 20th centuries. Let us look at the most important of these.
Imperialism was good because it would help the US economically. At this time, the US was getting stronger economically and it felt that it needed an empire to help continue that growth. It believed that an empire would be a good source of raw materials and a good market to which it could sell manufactured goods. Thus, imperialism would help the US economy grow.
Imperialism was good because it would make the US stronger militarily. This idea is closely connected with the military thinker Alfred Thayer Mahan. According to this idea, world power rested on sea power. If the US took an empire in the Pacific, it would have many naval bases from which it could project military power. This was important because the US needed to keep up with European countries whose empires were growing. Thus, imperialism would help the US become a world-class military power.
Imperialism was also perceived as good because it would help the people whose countries were being taken. This idea is often termed the “white man’s burden.” The idea here was that Americans (and other whites) were racially superior to the non-white people of Asia and the Pacific. By taking an empire, the US would be helping these people. It would bring them to a much higher level of civilization and prosperity than they could achieve on their own. In this way, imperialism was considered good because it would allow the conquered people to be connected to a superior civilization.
In short, Americans argued that imperialism would be a good thing because it would help the US militarily and economically and because it would help to improve the lives of the colonized peoples.
One of the other factors involved in the desire for empire was simply the ego of the leaders of the United States and the desire to do what other rich and powerful countries had done, namely to build an empire abroad. Seeing what the British had accomplished in terms of building an empire upon which "the sun never set" all from this small, isolated island in the Atlantic, other leaders wanted that same prestige and this helped to augment the other more practical motivations for imperialism that have been listed above.
In terms of military power, there were specific benefits to controlling territory abroad. Once ships were coal powered and then oil-powered, having bases scattered across the world at which your ships could refuel gave an enormous advantage to militaries wishing to project power farther than their own coasts. It also spread out the risk of losing access to a key natural resource involved in producing ships or guns or ammunition if you had more than one territory with those resources present.
As noted above, the economic motivation was also enormous. In just the four decades between 1870 and 1910, the value of American exports rose from around $350 million to over $2 billion. As the factories in the US rapidly expanded, they required those markets abroad to sell their goods, and the expansion allowed them to access new markets and maintain the military power necessary to protect the shipping and other physical assets necessary to maintain that kind of foreign trade.
Some Americans favored imperialism following Frederick Jackson Turner's promulgation of the so-called Turner Thesis. Turner's idea was that the American frontier had fostered the development of democracy and the egalitarian American spirit. As the Census of 1890 found that the frontier had closed, some historians and government officials believed that the United States had to begin to found an empire to provide an outlet for people to renew themselves (as they had previously on the frontier). Many saw the existence of a frontier as critical to the American spirit and to democracy itself.
Others who favored imperialism saw island territories as critical to the strength of our navy, and others desired an American empire to provide American producers with access to cheap raw materials and to markets for their finished goods. Finally, there were some people, including missionaries, who believed it was the burden of white people to "civilize" other nations and to introduce them to Christianity and to the American way of life.