(CNN) Editor's note: Hayder al-Khoei is research director at the Centre for Academic Shia Studies and an associate fellow of the Middle East and North Africa program at Chatham House . He is a member of the Atlantic Council Task Force on the Future of Iraq. The views expressed in this commentary are solely those of the author.

Iraq's ongoing military campaign to liberate the ISIS stronghold of Falluja is being sensationally framed in too much of the media coverage and commentary as a Shia versus Sunni war. Besides being inaccurate, this does a disservice to both the Shia and Sunni Iraqis working hand-in-hand to defeat ISIS

Despite some attempts to portray the campaign in Falluja as Iran-led , it is being led by the Iraqis themselves with support from both Iran and the United States. The tip of the spear in Falluja is not an Iranian-backed paramilitary group but the U.S.-created Counter Terrorism Service and its elite U.S.-trained Special Forces known locally as the Golden Division. These forces, besides being a mixed Shia-Sunni unit, are led by a Kurdish commander.

Who is actually on the ground?

More importantly, alongside both the Iraqi security forces and Shia paramilitaries, there are thousands of Sunni tribal fighters who are officially part of the state-sponsored Popular Mobilization Forces -- crudely, and again inaccurately, referred to in much of the Iraq commentary as "Shia militias."

A flashpoint of the Falluja coverage has been the Shia paramilitary forces who played a key role in not just blunting ISIS offensives but also in liberating much of the territory that has been retaken by Iraqi forces since the army's humiliating defeat in June 2014. These Shia forces are on the outskirts of Falluja and are not expected to be part of a ground assault into the city. But exaggerated fears are nonetheless constantly raised over what would happen if Iraqi Shias enter a Sunni-dominated Iraqi city.

It will be difficult to prevent retribution in any post-ISIS scenario and indeed there have been documented cases of this elsewhere in the country. But to continue to portray and place this violence within a broader Shia versus Sunni narrative is a gross simplification of the realities on the ground.

JUST WATCHED Iraqi military advancing on key ISIS-held city Replay More Videos ... MUST WATCH Iraqi military advancing on key ISIS-held city 03:31

ISIS systematically destroys the communities and cities they control through ruthless co-optation of the local population. When a city is liberated from ISIS, it is not just some Shia soldiers or paramilitary forces that seek revenge but also the Sunnis who lived under the tyranny of ISIS' occupation. It is the locals who have a much better understanding of who the collaborators in their own city and neighborhood were.

'Nation's struggle against terrorism'

When Tikrit was liberated by Iraqi forces in March 2015, there was a fierce inter-tribal struggle as locals took revenge against those who joined or helped ISIS. Even this episode of Sunni-Sunni score-settling was portrayed in much of the commentary as sectarian Shia-Sunni retaliatory attacks.

JUST WATCHED Iraqi military battles ISIS for control of Falluja Replay More Videos ... MUST WATCH Iraqi military battles ISIS for control of Falluja 01:52

The relentless focus on sectarianism when discussing Falluja led one Iraq-based journalist to tweet : "Falluja will take time, and will be very messy. But there's a current of poor commentary that's more sectarian than the situation itself."

At a time when sectarian dynamics is one of many factors fueling the crises in Iraq and beyond, it is important for Western journalists and analysts to not be more sectarian than the Iraqis on the ground actually fighting ISIS.

Iraq's fight against ISIS is not a sectarian war between Iraqis but a nation's struggle against terrorism.

It is not surprising that much of the regional media portray the events in Falluja as part of a broader sectarian war, especially when this serves the political agendas of governments that control these outlets. However, Western media coverage should be much more nuanced and sophisticated and not play into ISIS' hands who desperately want to make this a black-and-white sectarian war.