So because the USA has advanced weapons and other bases close enough to reach Moscow, it doesn't make sense that Putin/Russia would be concerned by NATO expansion even closer to Moscow, right next to their borders?
Having a state that you don't trust on your borders is not a justification for invasion. Hell, the UK trusts neither France nor Germany; both have attacked the UK, and planned to invade it, in the last 200 years. Lots of countries have neighbours they don't trust, but (on the whole) they don't launch unprovoked wars.
> Why doesn't it make sense?
Because Moscow has been in range of missiles for decades, Baltics and Finland and Ukraine in NATO or not.