Either Obama miscalculated and didn’t think the Turks would take advantage of the situation, or he let the Turks attack, thus betraying US allies in Syria (PKK).
Patrick Cockburn writes:
‘…the US was accused by Kurds of tolerating a renewed Turkish government assault on its Kurdish minority as the price for permission for US aircraft to use Turkey’s Incirlik air base against Isis jihadists for the first time.
“The Americans are not very clever in calculating this sort of thing,” said Kamran Karadaghi, an Iraqi Kurdish commentator and former chief of staff to the Iraqi President, Jalal Talabani. “Maybe they calculate that with Turkey involved on their side, they don’t need the Kurds.” [….]
The result is that the US may find it has helped to destabilise Turkey by involving it in the war in both Iraq and Syria, yet without coming much closer to defeating Isis in either country. If so, America will have committed its biggest mistake in the Middle East since it invaded Iraq in 2003…’
Turkey conflict with Kurds: Was approving air strikes against the PKK America's worst error in the Middle East since the Iraq War? – Middle East – World – The Independent.