That promise was cynical more than anything. In reality, Ukraine had the choice to give up nuclear weapons (which they couldn't deploy) or be invaded, either by Russia or the US. This was a preferable option.
As far as Russia, it's not a question of right or wrong. As part of the dissolution of the USSR, NATO made a tacti assurance TO Russia that they would not push until the border.
The occupation of Ukraine is a response to calls from Ukraine to align with the EU and NATO. Since neither organism allows entry if there is an active territorial dispute, so Russia created one.
From our position, it looks like Ukraine is only trying to defend from Russian imperialism, a much bigger power. From the Russian position, it looks like NATO coordinating a total encirclement of Russia and massing troops directly at its border and cutting off any hope Russia has to be able to assure its trade routes and even territorial security, against an openly interventionist empire.
Ultimately, both perspectives are true. NATO does seek to geopolitically checkmate Russia, which will make life for the average Russian citizen worse and increase the risk of a major war. At the same time Russia is indeed imposing on Ukraine.
Russia could be headed by anyone else under any even remotely functional system of government and it would go to amazing lengths to prevent Ukraine from joining NATO, no matter what. It's a simple matter that there is not really any choice available here.