Instead of addressing the issue, the US has been playing dumb by claiming that "don't worry mate, this is against Iran not Russia!"
Now, Russia plays its own geopolitical game too, of course. And you might believe that the US defence shield poses no danger to Russia. But you have to ask yourself, what does Russia believe? Because if Russia really believes the US is making moves to neutralise its nuclear threat, it's just a matter of time until it strikes, because like you said the alternative is to be wiped out from the world stage. Don't corner a rat. Very very concerning.
And this has been some ten years in the making, since the US withdrew from the Anti-Ballistic Missile treaty (which the US argued at the name was so that it could build its missile defence system). This does not seem conducting of stability in the world.
The problem with US foreign politics is that in the face of it they seem entirely ignorant of how their actions appear to the rest of the world (and what it might mean to their interests and how they would react to that).
EDIT: To clarify, I'm not saying the US was responsible for the entire Arab spring, but the Arab Spring and the mess it caused (when the initial euphoria had ended) are part of the fallout from the wars in Afghanistan and Iraq.
And we wonder that Russia feels emboldened to push its geopolitical interests? Russia needs to do that, or risk being wiped out from the world stage by an extremely aggressive US.