This fear has lead to Russia doing a lot of odd and silly things in their history. By putting anti missile bases in their sphere of influence, we are feeding this traditional fear. I honestly suspect someone in the Pentagon knew this, and that was the goal. The missiles won't stop a full on Russian attack (unless their capabilities are a lot smaller than we have been led to believe), but it will get them all fired up.
Read history and strategy. Russia is acting like Russia again.
There are many in Russia, including their permanent leader, 'KGB Putin', who would like to see a return of the Soviet Union. This will of course involve an invasion of their neighbors (again), particularly their former satellites, Georgia, Ukraine, etc. This is why they fear a NATO missile defense system. They also don't want it compromising their allies', Iran and North Korea, nuke programs.