In the 1890s, the United States was interested in Cuba for a variety of reasons. These reasons were generally connected to a desire for economic expansion and greater military power. There were also some altruistic or ideological reasons for being interested in the island.
The altruistic reason for American interest had to do with America’s attitudes towards colonialism. The United States, of course, had come into being when it rebelled against its European colonial masters. Therefore, many Americans were partial to peoples who were trying to break away from European colonizers. There was an independence movement in Cuba in the 1890s that attracted the attention and the sympathy of many Americans.
However, I would argue that the US was more interested in Cuba for selfish reasons. These selfish reasons were economic and military in nature. Many Americans saw Cuba was a potential source of economic gain. They knew that it had prosperous sugar plantations. They saw it as a potential market for American goods. These economic factors caused them to have interest in the island. At the same time, some American leaders were focused on expanding American military power. Following the doctrines of Alfred Thayer Mahan, they wanted to take possession of places around the world where they could put naval bases. These bases would allow the US to project its military power around the world. Cuba was seen as a good place to have a naval base, particularly since Americans were interested in putting a canal across Central America in either Nicaragua or Panama. A naval base in Cuba would help the US to exert more control over such a canal.
Thus, we can see that the United States was interested in Cuba both for altruistic reasons and for more selfish reasons having to do with economic and military power.