If Ukraine wanted to promise Russia that they would stay out of it, they could have done that without any US involvement.
Why should the US tell Ukraine how to conduct its foreign policy?
also, why Russia should decide on how other countries decide their internal affairs?
Ukraine doesn't need the approval of Russia to join or not join NATO.
Edit: I also want to add to this that the US is completely aware of the situation. They know exactly that their decision not to stop the expansion leads to a war. First, the US is not stupid. Second, there is a great example - Georgia, where war for the exact same reason took place. So, who's to blame here? Is it really Putin? My common sense tells the opposite.
There wasn't much support for NATO in Ukraine internally before seizure of Crimea. Who's in the wrong here? Hmm, I don't know.
Everything started in April of 2008, during the Bucharest Summit Declaration saying that "NATO welcomes Ukraine’s and Georgia’s Euro-Atlantic aspirations for membership in NATO". Russia immediately said that this is not going to happen because it affects their security - and it DOES make sense, doesn't it? That led to a war in Georgia. Today it's a war in Ukraine, my home country.
Once again, Putin is just a side effect. The core, the _root_ cause is the US's maniacal NATO expansion aspiration.