That's because Ataturk is symbol of "Turkish nationalism" and for 80 years mistreatment of kurds has been carried out by mostly Ataturkian establishment.
I have lived in Netherlands for a few years and among Turks (which are a huge immigrant group) there. You do not believe the amount of hatred a third generation immigrant Turk has towards Kurds. You cannot believe the amount of nationalism a thirds-generation Turk has and how they praise Ataturk.
Having said that, the issue is that there many Turks who are actually quite educated and secular. Some are intellectual leftists, anarchists, liberal, and Marxist and they do support Kurdish quest for having a better situation in Turkey.
Another thing that this Chinaski or other Iranians are not aware of (because they still international relations from the perspective of cold war era, not knowing that the world has moved on!) is the whole notion of the 'Turkish Deep State'. Many seculars, nationalists and former military and intelligence people fall within that theory. Whether it was Erdogan and his gang on power or if the ataturkian seculars where on power, governments even with different ideologies seek to pursue their national interests. For Turkey, on the surface Erdogan and his gang do it. But in the background the people in Turkish deep state are also running the show. They do not want Kurds to gain autonomy because they know that would not be good for Turkey.