>>330The Kurds are fighting against Turkey, which has historically oppressed them, and insurgents like Da'ish which have been supported by Turkey, Saudi, Israel, and the West to overthrow Assad but now these insurgents want personal territorial gain.
And supplying Kurds with armament will backfire because that and training will lead to an autonomous Kurdish state which would definitely cause major problems in Iraq and Turkey and Iran would intervene. The West once again would be adding fire to a delicate situation and cause things to collapse, finding itself to take the majority of the blame from people in the region who would just become angrier at it.