Basically Putin wants Russia to be respected, he obviously misses this in seeing NATO grow ever nearer to Russia's borders (see baltic states, Poland etc.) despite the pledges of western states made to the (then) CCCP.
The USA argues that this eastern shift of NATO is not violating the pledge since the CCCP does not exist anymore. They also insist of every country having the freedom and right to decide to join any military treaty, anytime.
The first is a lawyer's argument which is somehow correct theoretically even if it feels definitely morally wrong; the second has more weight.
Ok Russia tries to influence Ukraine politics, but so does the US.
Anyway, the guarantee or assurance Putin wants is that there is no
additional country at Russia's borders joining NATO, read: Ukraine.
Let's be honest, Ukraine is neither financially ready or fit enough to join the EU, nor "ripe" to join NATO. It is corrupt even without Russia's or the US's external influence and has to get a grip on its own situation first. Interference from abroad will not help them as a nation.
Would it have been so impossible for 'the west' to agree to this not joining the NATO, at least for the next decade? Especially in this (for the west) weak situation?
Russia could be a valuable partner against China, just in case..