Because the allies during ww1 promised the kurds a state if they took up arms against the Ottoman Empire which they gladly did.
Once the Ottomans collapsed and Ataturk won the Independamce along with putting down several kurdish rebellions in the independance war which kurds tried to make themselves a country the Allies gladly abandonded them because they no longer had any use.
Dream of kurdistan are nothing more than delusions in which the British promised every damn ethnic group in the Ottoman Empire a state.
This what happens when you promise everybody something which clashes with the other promise you made to Assyrians, Jews, Arabs, Druze and Alawites.