Southern expansionists wanted to add more territory to the US so they could spread the pro-slavery territory over the slave-free territory. Because of that, they hoped to bring Cuba and other territories to the US and enlarge the empire of slavery.
Also, during that time, Haiti had a slave revolt and overthrew their masters and created a black republic. The Slaveowners did not want that since they wanted to expand pro-slave territory.
Also, they believed that Britain was interested in the Island because of sugar and since Britain prohibited slavery in their colonies, Cuba would be free.