My understanding is that one of Russia's concerns with the expansion of NATO into Eastern Europe is the US deployment of anti-ballistic missile systems in countries like Poland. The US wants to be able to do boost-phase or mid-flight intercept on Russian ICBMs. From Russia's perspective, that upsets the strategic balance of power and gives NATO the upper hand in a first-strike nuclear exchange.
I wonder if the deployment to Cuba is meant to play into American politics—we are in an election year. In WWII a strike on American soil fired up the people to support the war effort. Today, a similar attack might just demoralize the American populace and make any war immediately unpopular. We're so used to all the fighting happening "over there," and patriotism seems to be low.