Understood, it is the influence of the Iraqi Kurds that is feared in Turkey, Iran and Syria. A spillover effect from an uprising or autonomy. Turkey would have to be guaranteed that any Kurdish rebellion stayed in Iraq or would not affect Turkey. Turkey is smart enough to know that guarantee cannot be made.
The question then remains how can we grant autonomy to the Kurds and keep Turkey as an ally? Training the Kurds to take on Iran can’t help.