The correct full question seems to be: How did the activities of the US in Latin America set the stage for war with Spain?
The answer to this question is:
The US had since the Monroe Doctrine, issued in 1823 but coined like this only in 1850, declared that any influence on the American continents' policies by European powers should be seen as attacks on the US themselves. This was a way to keep American continents as the US' sphere of influence only.
When the Cuban war of independence started, the US political leaders supported Cuba publicly because of the Monroe Doctrine and also because the country had commercial interests in Cuban territory.
There was also American interference on Latin America activities by newspapers that made <em>yellow journalism</em> -- that is, many sensationalist reports on the war of independence about Spain's atrocities that created public support for American intervention.
