Nobody has ever suggested that there was a prospect of a NATO invasion of Russia. That is crazy talk; it'd be the end of civilisation in the northern hemisphere. They aren't deploying troops to ward off a NATO invasion, that is what the ICBMs are for.
So what's really going on? Well, Putin said "rudely". Russia feels insulted because everybody wants to be in NATO, and nobody wants to be Russia's buddy... if you take Putin's words at face value.
If you don't, then I think Putin is terrified of Ukraine's revolution against a Russia-friendly leader. He doesn't want a western-friendly revolution in a culturally-Russian-adjacent country to succeed - there's too much chance that Russians might decide that they like the idea.
The way the Ukraine war has played out makes it pretty clear the Russians did have legitimate concerns. When the US invades Iraq with no moral justification, everyone moves on. When Russia invades Ukraine with no moral justification we see a similar response from most of the world ... except NATO that goes in and orchestrates what Wikipedia suggests are half a million casualties of the Russian armed forces [1].
Why might Russian military planners feel this is a threat? Because they can count corpses and they're not stupid. If you want to argue that they underestimated the threat NATO posed them in Ukraine and so Putin was lying that is one thing, but if so his propaganda happened to be truer to reality than he thought because he made a great point. NATO is out to get the Russians.
[0] https://en.wikipedia.org/wiki/Monroe_Doctrine
[1] https://en.wikipedia.org/wiki/Casualties_of_the_Russo-Ukrain...
Because the major point of that infrastructure is to kill lots of Russians if they invade.
> Why might Russian military planners feel this is a threat? Because they can count corpses and they're not stupid.
Because they can count corpses after they invaded.
The logical conclusion was "don't invade", not "hurry up and invade while you still can".
Except there was no "full military integration" in the works, or even any "gear" deployed in Ukraine before Putin started throwing his massy hissy fit in 2014.
Because the major point of that infrastructure is to kill lots of Russians?
The point is to gently remind the current regime of the borders of NATO states, and of this thing known as Article 5 of the North Atlantic Treaty.
> If NATO anxiety was the primary factor for the war in Ukraine, Russia wouldn't be so blasé about draining troops and hardware from its borders with NATO countries to throw them into the meat-grinder
