I'm not sure it was Ukraine that made the decision. Rather it was a small group of unelected right wing radicals that came to power after the Euromaidan, and promptly made strong moves intended to force the country down a certain path. Remember, Turchinov and Yatsenyk hail from Svoboda, a border-line neo-Nazi group (they cleaned up their website during the Euromaidan, before that it had lines on there about cleansing Ukraine from Russians and Jews). Neither Svoboda nor Right Sector, could win an election in Ukraine. So who really made the decision?
That's what I heard on Russian national television, that the government is neo-Nazis. Unfortunately I was disinterested in the topic when it was still rolling.
The west treated it as a dangerous but still fringe group, even those who had no side to pick in the conflict.
Regardless, when you eliminate all foreign influences (i.e hard influences, like appointed government officials), you get a sovereign decision. And for the better or worse, a sovereign decision must be respected. There are many reasons to believe a shift to NATO and EU and the west in general, is logical from a Ukrainian standpoint regardless of the government's ideology, with the sole exception of being a pre-2014 vassal state.
By supporting Ukraine, the west basically grooms a nation that could become truly democratic within 20-30 years.
Russia could actually show much more peaceful intent by respecting this decision, thus maintaining economical interests in Ukraine, and increasing economical and resource dependence of the west on Russia.
This would in turn be a much more powerful deterrent against the west, as evident by German inaction on Ukraine.
This shows Russia pretty much made a gamble with Ukraine, and an actual war would mean the gamble is very likely lost, and war is a last minute attempt at remedy.
The west can avert the war via many means. Arming Ukraine is definitely one of them (albeit likely not enough).
If a war is averted, Russia's chances of redemption are reduced significantly, as it will further deter western nations from economical dealings with it, which further reduces Russia's deterrence in turn.