There are at least three reasons for this.
First, because of its history, the US tended to be sympathetic to groups that were rebelling against a colonial government. Many Americans thought that a country that had itself rebelled against a European monarchy should help rebels who were doing the same. In this sense, the US saw the rebellion as a cause for war due to ideological reasons.
Second, there were those in the US who were looking for any excuse to go to war. These people, like Theodore Roosevelt, believed that the US was growing soft. They believed that the nation needed to have a war to make Americans tougher. This group saw Cuba as a convenient way to test and enhance American masculinity.
Finally, there were those who wanted the US to have an empire. This motive was mixed up with the previous motive. These imperialists felt that the US needed to keep up with the European countries that all had and/or were gaining empires.
For these reasons, an issue that was seemingly internal to Spain became a cause for war in the US.