In fairness here, the main reason Russia are scared of NATO on their border is specifically because the West and Europe in particular (technically France and Germany in particular) have a habit of invading them. You and I know that's not likely to happen again, and definitely not anytime soon, but I can see why the average Russian may consider it a realistic concern. If you lose 30 million people to invading forces in three world wars started by western Europe the natural result is to become wary of western Europen.
I've heard that sort of argument before and it just strikes me as being complete BS, Putin knows full well the flippin EU isn't going to mount an invasion.
It's like saying Poland should be worried about a German invasion right now or we should be worried about the Spanish and French navies etc... All countries in Europe have been at war or faced the threat of invasion during the same time periods, there isn't anything special about Russia there.
They don't like that those countries have fallen within the Western sphere of influence, it highlights their own failings, previously it was communism where they were desperate to keep the citizens of the Soviet Union separate and now it's this sort of dictatorship/gangster government under Putin.
Estonia, Latvia and Lithuania are all success stories, they don't want Belarus and Ukraine to go that way and become aligned with the west, become more successful too - the threat isn't one of military invasion, the threat is the domestic issues and pro-western or pro-liberal opposition leaders gaining prominence and undermining the current regime under Putin.
Ukraine is a larger country and Ukrainians have strong cultural links to Russia, if they become more successful and more secure (and can't be intimidated as easily via NATO membership) then that can influence things domestically in Russia.
They've kept domestic opposition in check so far in part with control of the media, corrupt elections etc.. but a stronger, pro-Western opposition is a possible outcome from Ukraine going that way. Also the revolutions, they're **** scared of what they saw in Ukraine in the Orange revolution in 2004 and the Maidan revolution in 2014 (that's what triggered the military reaction really), that's the other risk if the Russia population starts becoming more pro-Western, influenced by neighbours, they might still be able to fiddle election results but if you have a mass of popular support for change within the population then rigged elections aren't always enough, that sort of revolution is a big risk for them too.
Everything else seems like a weak excuse in comparison, it's a corrupt dictatorship and corrupt dictatorships are especially worried about being overthrown/kicked out of power.