You don't get it. By supporting conservative, Sunni and pro-Turkish groups among the Kurdish population we have the opportunity to fight back PKK in Turkey and within the separatist Kurdish ideological frame abroad.
It is a simple calculation. If we support Barzani, what does we get in return? Oil, gaz, weaker PKK, delimited Iranian influence. This debate is very advanced in the Turkish society. Some are even ready to accept a pro-Barzani Kurdistan (North Iraq) within the borders of Turkey with extensive self-government rights.
To tell the true, it is not in our interest to make such a farreaching step at this moment. But, who knows, the hole situation could change even tomorrow. And, no, Iran won't fight Turkey. In fact, Tehran couldn't do anything in this case. You may handle the Kurdish terror groups in Iran so far but this is Turkey we are talking about. You won't be able to fight the Kurds, contain the
Turkish-Azeri irredentism, kill the Balouch movement, stand up against GCC members and handle Israeli/US interventions and support Shias abroad at the very same time.
Why do you think Turkey has a large base in North Iraq? Why do you think they are training Peshmergas, Shia Turkmens and Sunni Arabs?