I don't know, may be Russia see NATO + US as a much bigger threat than how NATO see Russia as a threat. Or may be NATO have some other ways of dealing with this threat.
Or maybe Russia see eastern and central Europe as their sphere of influence, which they lost. And now they're using any excuse to try to re-establish that.
What kind of NATO danger did they expect from Georgia?
Russia had zero reason to see de-militarised Europe as a threat.
That's certainly true now, even if it wasn't true before. So why would Putin act in a way that was absolutely guaranteed -- win, lose or draw -- to fortify and entrench NATO's presence on Russia's borders?
His NATO excuse never made any sense. Don't invade anybody, and you have nothing to fear from NATO.
May be he is/was worried about USA