I think the story is more like small fish would rather hang out with big fish than with medium fish, but medium fish doesn't like big fish, therefore medium fish eats small fish. NATO is a military alliance and its stated purpose is to defend states in case of an attack of a third party. NATO has no doubt overstepped this mandate more than once and led military operations where considering a member state attacked is a pretty far stretch. In practice military campaigns are carried out calculating that the rest of the world will not react. Everybody does that. But Russia miscalculated. Much of the world did react, which perhaps came as a surprise to Russia because there was no serious reaction when Crimea was annexed.
Medium fish wants to be big fish, and this makes the current situation more dangerous than during the cold war when there was big fish versus big fish. Now medium fish has to prove itself.
Medium fish invaded little fish because medium fish didn't want big fish and small fish to be friends. But that is not a reason for invasion. So a pretext of fixing a nazi problem was found. Ukraine was hardly perfect, but Russia "helping" Ukraine to fix Ukraine's problems is somewhat like somebody helping out his neighbour's weed problem by bulldozing through his house into his garden to remove those weeds once and for all, without asking the neighbour.