...and an aircraft carrier off your coast capable of scrambling interceptor aircraft from much closer to the threat is the definition of a defensive system.
No, its not. At best its a Dual purpose defensive/offensive system.
A purely defensive system would be something like Static AA systems, Anti-Missile systems, fallout shelters and the like.
They can't be used to project powers elsewhere.
An Aircraft carrier has no real use except as an offensive system. Even in the example you are using its an offensive system, its projecting force outside of your territory.
A counter-offensive system is not a defensive system. Its just an offensive system you are holding in reserve, no different than ICBMs, the sole purpose to attack others (regardless of who started it).
The Polish anti-missiles are not a problem because they can hurt Russia, they are a problem because the limit Russias ability to launch strikes on others.
Russia is getting antsy because its like one side in a mexican stand off suddenly donning a bullet proof vest. The vest is no danger to you, but it means if it ever does come to blows, the other person would live through it, and thus doesn't need to fear you anymore.
