The battle for Mosul seems to be going better than media reports indicate, which focus on Iraqi casualties. A lot of jihadis have died so far trying to hold Mosul. The slow pace is to keep coalition air and Iraqi ground forces in sync to counter ISIL suicide bombers. Civilian casualties appear to have been kept down. And the question of whether jihadis will fight to the death will depend on the quality of ISIL frontline leadership--many of whom already left the city.
The Iraqis might yet defeat ISIL in Mosul this year--which would be different than completely clearing jihadis who may go underground. But ISIL would be denied Mosul which would pass to government control.
The most disturbing aspect of the campaign against ISIL is Iran's growing influence in Iraq:
[Iranian Pasdaran (aka Revolutionary Guards) General Qassem] Suleimani was described as arriving in Iraq on June 10th 2014 and then bringing in thousands of Iranian and Lebanese (Hezbollah) advisers, experts and combat commanders to organize an effective response to the ISIL offensive. ... Suleimani belongs to IRGC (Iranian Revolutionary Guard Corps) and commands the Quds Force (similar to the U.S. Special Forces, but which specializes in supporting Islamic terrorists not fighting them). It was Quds that helped form Hezbollah in the 1980s and built that Shia militia into a major force within Lebanon. Iraqis now fear Quds will try and do the same thing in Iraq and even many Iraqi Shia don’t want that.
Recall that a major reason I wanted to stay in Iraq after 2011 was to help Iraq resist Iranian pressure to do what Iran wants. Without us on the ground to help with that, the Iraqi government undermined their officer corps by selecting men loyal to the government without regard to competence. That alienating Sunni Arabs as well.
The result was that ISIL rose with the support of Sunni Arabs in the first half of 2014, the ability of the Iraqi military to defeat ISIL dropped dangerously low, and Iran entered Iraq in some strength to pursue their policy of pressuring Iraq to be compliant with Iranian wishes.
America is reportedly committed to staying in Iraq after Mosul is liberated, but we have a lot more work to do than if we'd just been there the last 5 years.