The missile defense shield creates a situation in which the US could send missiles to Russia (nuclear or otherwise) and Russia would not be able to respond. Which makes the missile defense shield an offensive rather than defensive measure, in that it eliminates deterrence against a US attack on Russia.

The Russians have every reason to feel threatened by the US missile defense shield being place in those countries. Russia did suggest an alternative site for the missile defense shield, that would have been more effective in deterring missiles coming from countries like Iran, and would not leave the Russians feeling threatened (one of the Stans, if I recall correctly), but the US is determined to put the shield where it will be a threat to Russia.

So it is certainly true that it only takes one side to start a Cold War, but it is the US that is starting it, and not Russia.