Question

Why did the U.S. get involved in the Cubans’ fight for independence from Spain?

Answer 1

"U.S. interest in purchasing Cuba had begun long before 1898. Following the Ten Years War, American sugar interests bought up large tracts of land in Cuba. Alterations in the U.S. sugar tariff favoring home-grown beet sugar helped foment the rekindling of revolutionary fervor in 1895. By that time the U.S. had more than $50 million invested in Cuba and annual trade, mostly in sugar, was worth twice that much."
So, it seems like the US got involved because the US was interested in allying with cuba once they had their independence, to benefit from their bountiful amounts of sugar.

Answer 2

"Spain’s brutally repressive measures to halt the rebellion were graphically portrayed for the U.S. public by several sensational newspapers, and American sympathy for the rebels rose. The growing popular demand for U.S. intervention became an insistent chorus after the unexplained sinking in Havana harbour of the battleship USS Maine (Feb. 15, 1898; see Maine, destruction of the), which had been sent to protect U.S. citizens and property after anti-Spanish rioting in Havana."
This adds to it, and basically says that America grew sympathy for the Cuban rebels, and once the USS Maine was sunk by Spain, the public pressured US government to intervene in the war.