What is Turkey's deal in Mosul?

The operation to save Mosul, Iraq's second biggest city, from the Islamic State of Iraq and the Levant (ISIL) has begun. It is led by the Shiite-dominated Iraqi army, Shiite militias, Kurdish Peshmerga forces, some Sunni forces trained by Turkey, and of course the United States, which is coordinating the whole effort. Turkey, however, is rather angry about what is going on. Why? What is really going on? 

Before giving you an answer, I must underline a few facts that go against the common narratives about Turkey in the Western media. 

One narrative is that Turkey is somehow lenient on, or even supportive of, ISIL, the most brutal terrorist force the world has recently seen. But this is not true, as you can see in the Turkey-led military campaign going on in our neighboring country: Syria. Since last August, Turkey has been actively fighting ISIL through its military incursion into northern Syria. Last weekend, the Syrian Sunni militia supported by Turkish forces even liberated Dabiq, the city with a major religious (in fact, apocalyptic) importance for ISIL. 

In Iraq, too, Turkey is a part of the anti-ISIL campaign, and only wants to engage in it more deeply. The only thing is that Turkey is also concerned about the "Sunni base" on which ISIL has been operating. (The Turkey of today, after all, is also unmistakably Sunni.) In Mosul, Ankara is worried that the Shiite militia that is eager to take the city could engage in vengeance, terrorizing the population. Given the visible brutality of some of those Shiite militias (check YouTube, if you are not too averse to gory images) that is not an unfounded worry. 

The other fact I must underline is the complicated nature of Ankara's take on "the Kurds." If you read Western media, you often...