Not sure where you're getting this idea that this is what Obama did.
He was smart. Journalist Aaron Mate touches upon why Obama refused to arm Ukraine in an article he wrote a few months after Russia's military operation in Ukraine began:
In 2019, Zelensky was elected on an overwhelming mandate to make peace with Russia. As Stephen F. Cohen warned that year, the US chose to side with Ukraine’s far-right and fuel war.
scheerpost.com
Quoting the introduction:
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On a warm October day in 2019, the eminent Russia studies professor Stephen F. Cohen and I sat down in Manhattan for what would be our last in-person interview (Cohen passed away in September 2020 at the age of 81).
The House was gearing up to impeach Donald Trump for freezing weapons shipments to Ukraine while pressuring its government to investigate Joe Biden and his son Hunter. The Beltway media was consumed with frenzy of a presidency in peril. But Professor Cohen, one of the leading Russia scholars in the United States, was concerned with what the impeachment spectacle in Washington meant for the long-running war between the US-backed Ukrainian government and Russian-backed rebels in the Donbas.
At that point, Ukraine’s Volodymyr Zelensky was just months into an upstart presidency that he had won on a pledge to end the Donbas conflict. Instead of supporting the Ukrainian leader’s peace mandate, Democrats in Congress were impeaching Trump for briefly impeding the flow of weapons that fueled the fight. As his Democratic allies now like to forget, President Obama refused to send these same weapons out of fear of prolonging the war and arming Nazis. By abandoning Obama’s policy, the Democrats, Cohen warned, threaten to sabotage peace and strengthen Ukraine’s far-right.
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I think it's a great article. Aaron then launches into the main theme of his article, how the U.S.'s encouraging of the far right in Ukraine led to Zelensky's turnabout from peace candidate to war cheerleader. He starts with how things were back in 2019:
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“Zelensky ran as a peace candidate,” Cohen explained. “He won an enormous mandate to make peace. So, that means he has to negotiate with Vladimir Putin.” But there was a major obstacle. Ukrainian fascists “have said that they will remove and kill Zelensky if he continues along this line of negotiating with Putin… His life is being threatened literally by a quasi-fascist movement in Ukraine.”
Peace could only come, Cohen stressed, on one condition. “[Zelensky] can’t go forward with full peace negotiations with Russia, with Putin, unless America has his back,” he said. “Maybe that won’t be enough, but unless the White House encourages this diplomacy, Zelensky has no chance of negotiating an end to the war. So the stakes are enormously high.”
The subsequent impeachment trial, and bipartisan US policy since, has made clear that Washington has had no interest in having Zelensky’s back, and every interest in fueling the Donbas war that he had been elected to end. The overwhelming message from Congress, fervently amplified across the US media (including progressive outlets) with next to no dissent, was that when it comes to Ukraine’s civil war, the US saw Ukraine’s far-right as allies, and its civilians as cannon fodder.
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