When Obama left, it appeared to be one of those better times. Yet it led to chaos and conflict regardless.
The Kurds would've expected air support from the Americans against Turkey. But lets be realistic here. Turkey is a NATO ally. Are the Americans truly going to fight against a country that they've forged a military pact with? Is it preferable to risk one of those 100 troops being a casualty of Turkish aggression, or rather just move them away from the chessboard?
I'm sure that this is difficult for many Americans to fathom, due to media portrayals, but it is Turkey that is in fact, America's official ally, whereas the Kurds have largely been officially denounced as terrorists (which, to be fair, they have been, with suicide bombings targeting civilians, etc.). To support the Kurds against Turks would in fact be America going against its "promises", its official policy, and not vice versa. And we are talking about long-term policy, not just short-term "convenient allies" in a fight against a bigger villain (ISIS).
Now I can personally fully agree that Turkey is a villain here, but I've been saying that for a very long time. Which is why I believe they should not belong in NATO. But they do. And since people seem to be very fond of NATO (even if Trump himself may not have been), they have to live with those loyalties, above whatever loyalties are only forged out of circumstances (such as those with the Kurds).