The only reason the Ottoman Empire existed for its last 300 years was because of maneuverings of European powers. The empire was basically a pawn of Germany, Russia, England, France and pretty much every European power in their various quests for world domination.

How western powers orchestrated the political maneuverings of The Middle East were radically changed after WWI. Western powers stopped pretending that The Ottoman Empire was a thing divided up the maps of the middle east into different countries that they could manipulate.

During that divvying up there was a push to establish a Kurdish state from the carcass of the Ottoman empire but it fizzled out. I guess no major power in the divvying up process saw any value in giving the Kurds a state.