While the Kurds are seen as the most effective rebel force in Iraq and Syria, they are internally divided and that factor is often ignored or underestimated in the West. While the autonomous Kurdish area of northern Iraq has a somewhat united armed force (the Peshmerga), many of the other Kurdish groups up there are divided by clan and politics. Thus the PKK (Turkish separatists) are difficult to work with, in part because the Turks are hostile to any Kurdish group that gets too cozy with the PKK. Same with the Syrian YPG, but to a lesser extent. Then there are the Yazidis, who Kurds largely regard as Kurds but ones who have developed very different religious and social customs. Most Moslems consider the Yazidis heretics or pagans.
In northern Iraq the autonomous Kurds want more autonomy (but short of declaring themselves a separate state, which would enrage Turkey) while they are turning into a dictatorship run by the Barzani family. The Iraqi Kurds had long been divided into warring clans, the two largest of them led by the Barzani and Talibani families. Since the 1990s, the Barzanis have emerged as the most powerful clan and they are behaving more like a dictatorship (corruption, suppression of dissent, and rigged elections). Popular anger against this among Kurds is increasing. Despite that, Kurds living outside the autonomous area continue to move back to the Kurdish region. Even the Iraqi Army, which was rebuilt after 2003, with a core of experienced, loyal, and reliable Kurdish troops is losing many of its Kurds. It’s mainly a matter of not wanting to get caught up in the war between Shia and Sunni Arabs.
Yet the Iraqi Kurds are still a formidable military force. Since the early 1990s the Iraqi Kurds have been autonomous (with British and American help) and they had always been more effective soldiers than the Iraqi Arabs. The Kurds still suffer from tribal and clan divisions as well as corruption, but to a much lesser extent than the Arabs. Thus a disproportionate number of Western trainers are being sent to the Kurds, who are only about a fifth of the Iraqi population. The Kurds are considered reliable enough to work with Western commandos and protect ground control teams (that can call in air strikes). Kurds regularly assist the American and British commandos in carrying out their most dangerous tasks; reconnaissance inside ISIL territory. But the Kurds have not got the manpower for large scale operations.
The Kurds have had more than their share of bad breaks. Like many mid-size ethnic groups the Kurds were never able to establish their own nation and for thousands of years have been subjects of one empire (Iranian, Roman, Turkish and so on) or another. A century ago they were part of the Turkish homeland because the Turks recognized the Kurds as worthy allies (but still part of the empire). Turks even like to call the Kurds “mountain Turks”, a name the Kurds do not like at all. After World War I the Kurds living near the Turkish city of Mosul found that they were no longer Turkish subjects but now part of the largely Arab nation of Iraq. This was done by the victorious allies (mainly Britain and France) to deny the Turks (now a country, not an empire and reduced to its present borders) oil, which had recently been discovered in the areas around Mosul and Kirkuk. Needless to say the Arabs, long unwilling subjects of the Turkish Empire, did not welcome the Kurds (who were often the Turkish enforcers when the Arabs got out of line). The Turks recognized and used Kurdish military skills and Arabs feared the Kurds because of that. Meanwhile, the Kurds in general were angry that the allied promise of a Kurdish state (once the Turks were defeated) was not kept. That was mainly because the Turks, now pushed back to their homeland, made it clear that there would be a major fight if the allies tried to keep all the promises made at the expense of the Turks. The war weary allies backed off after a brief war and the Kurds were screwed again.