Because that's the effect of this policy would be. Setting up a No Fly Zone in Syria would require ordering the Air Force to shoot down Russian planes. And for what? To stop Putin from bombing Al-Nusra, an Al Qaeda affiliate?
This right here, Hillary's hawkishness, is the reason why she's the worst candidate in the primary. She's not any better than Biden on things like Wall Street and healthcare, but she's far, far to the right of him on foreign policy.
I'm sure Clinton doesn't actually mean this. I'm sure if she was President, she'd be acting like Obama is in this situation. But this kind of pandering to win votes by looking tough should be rejected by Democrats. We're not Republicans.
UPDATE: The Christian Science Monitor agrees with me:
Here’s the problem: Russian warplanes are now based in Syria and flying sorties through Syrian airspace to bomb opponents of Syrian ruler Bashar al-Assad. The US isn’t happy about that, and it’s made the military situation there a lot more volatile. It’s also made the issue of the no-fly zone more problematic.
Sure, calling for a no-fly zone is an easy way for a presidential candidate to differentiate themselves from the White House (the administration has long rejected the idea). It makes you look tougher and more forceful than the folks currently running US foreign policy, perhaps.
That’s one reason why other GOP hopefuls have pushed no-fly zones in the past.
But a unilaterally-declared Syrian no-fly zone could pull US aircraft into actual shooting combat with forces from the only other country that possesses more than a thousand nuclear warheads. That’s a situation lots of military experts think is, ah, best to avoid.
I suppose we'll have to add them to the list of publications that have revealed their role in the Vast Right Wing Conspiracy (nevermind that Clinton is agreeing with Fiorina against Obama).