The correct answer to this open question was the following.
The difference in the perspectives of Americans and Cubans in regards to the Battle of San Juan Hill is that the Cubans were tired of the Spanish monarchy presence in the Island of Cuba, but had no means to get rid of the Spaniards and its powerful army. The American point of view was that the United States had the exclusive right to intervene and take care of the issues in the American continent, not the Europeans, that is why the First US Voluntary Cavalry, led by Theodore Roosevelt, tried to recapture Santiago de Cuba. To accomplish this, they had to fight a severe resistance in the Battle of San Juan Hill on July 1, 1898.