The Government of Iraq was blackmailed into granting the Kurds some degrees of autonomy. In fact, the Kurds hardly listen to Baghdad anymore.
The Government of Iran is opposed to any form of Kurdish government or succession.
The Government of Syria is similarly opposed to any kind of self-governing Kurdish country.
Turkey is simply one of 4 countries which the Kurds want to take territory from, to establish their own state which one presumes would be based along the lines of Marxism-Leninism and oligarchies. For countries that will lose out, this is unacceptable.