What is the semi back handed hate against Kurds? How come they don't have a country yet being that the PKK is pretty powerful?

I suck at history or geography but: https://en.wikipedia.org/wiki/Kurds

1. geographic region spanning southeastern Turkey
2. PKK considered as terrorists by Turkey since forever
3. Turkey seems to be the only country to hate everyone except their own expatriates when it comes to voting for good old Erdogan

Their claimed territory spans 3 countries, which doesn't help their separatist movement. Those countries are now incentived to coordinate suppressing their separatism together.

Nations typically don't like separatist movements from themselves. Maybe there's more to it for why those countries don't like the Kurds, but that's probably plenty by itself.