Having said all that, the biggest mistake we made after the Cold War was NOT inviting Russia to join NATO and still treating Russia as the bad guys.
We did float an invitation, but it wasn't ever taken seriously by either side. A PR stunt for us, and it was probably counter-productive, with Russia largely seeing it as an insult, and a statement that the U.S. and NATO now saw them as weak after the dissolution of the USSR.
There is less than zero chance Russia would have ever joined NATO, at any time whatsoever between the dissolution of the USSR and the rise of Putin. None. Nada. Zilch.
1. What is the simplest and strongest reason, it would completely go against Russia's national/cultural identity seeing themselves as a superpower, or a one-time superpower, or being a superpower again.
2. (perhaps a subset of #1..) It would completely negate Russian ambitions in the region or the world, even if they could or otherwise wanted to participate in NATO, they wouldn't be able to prop up Syria, Iran, or push the levers of power as they saw fit.
3. No matter what kind of assurances or "seat at the table" or a U.N. Security Council-like veto power. Russia was given within NATO, everyone knows that NATO is run by the United States and all it's other members are to some degree or another subordinate, and Russia would never ever stand for it. And even if some sort of iron-clad deal could be worked out to make Russia on a "more equal than others" standing like the U.S. enjoys, they'd always fear that NATO integration and politics would eventually weaken them into subordinate status. Or, they know full well the other NATO members would never take orders from Russia like they do the U.S.
4. Arguably, probably the most pragmatic and strategic reason if all the political and cultural ones could be swept aside... If they joined NATO, and not in some flim-flam way, but
really joined NATO, at the same level of inclusion as the U.S. and the U.K. have... there's no way China would stand for it. And Russia would be in the uncomfortable position of sharing something like 4-5000 miles of border with China as a NATO member. And if America/Japan/Taiwan etc. got into a hot-war with China, Russia would be dragged into it.
5. NATO member states (Well... except for Turkey I guess, but we wanted IRBM's and bombers on the USSR's doorstep.) are all relatively open democracies or representational or parliamentary republics of one sort or another that has ultimate civilian control over their militaries. The civilian government determines the funding and the broad strategic and smaller tactical goals of their nations militaries. Russia never ever had a time in it's existence since the Czars where that was the case, where the military has always functioned as a de-facto branch of their government either under Communism and the USSR or now under the Russian Federation. And to try and get Russia's military completely subordinate to civilian control would stand a good chance of creating a coup.
I agree it would be cool if we could get Russia into the fold, and kinda-sorta set up the "CoDominium" like in the Jerry Pournelle military sci-fi novels, and keep the rest of the world (especially China) in check, and never have any part of it ever act up into a broader hot-war again, but it just isn't in the cards.
