Well, that question ignores the basic fact that we won the Iraq War.
And it requires you to forget that the Iraq War did not cause chaos in the Middle East--it being a cauldron of instability already that required the smallest American regional unified command (CENTCOM) in geographic scope to cope with it using military means.
But let me address this "biggest mistake" claim:
On May 15, 2003, one day after he arrived in Baghdad to head the Coalition Provisional Authority, [L. Paul] Bremer issued CPA Order No. 1, which barred members of Saddam Hussein’s Baath Party from all but the lowliest government posts. The next day, he issued CPA Order No. 2, which disbanded the Iraqi army.
With those two orders, the future of Iraq was doomed, the already-likely failure of the American mission was sealed, and the prospect of a sectarian civil war—enveloping not only Iraq but the entire Middle East—became nearly inevitable.
Bullshit.
De-Baathification of Iraq in 2003 was as necessary as de-Nazification in Germany in 1945. The party was the tool of minority Sunni Arab oppression and exploitation of the Kurds and Shia Arabs. How would the Shias have fought on our side if they thought that the invasion of Iraq was just for the purpose of putting more pliable Sunni Arabs in charge? Wouldn't that have just pushed them into the arms of Shia Iran? How, as I asked, would the 2004 Sadrist-Sunni dual uprisings have played out if the new Iraqi security forces had been controlled by "former" Baathist officers and riddled with Sunni Arabs. Face it, there would have been problems either way with this tough choice, and we made the right choice.
Further, consider that in 2007 after the Sunni Arabs finally gave up and joined the Awakening, the Iraqi government paid off the former Saddam officials--yet that didn't stop them from joining with ISIL in 2014. Nor did the reinstatement of 20,000 of Saddam's officers to the military in 2010 make them loyal servants of Iraq. Huh.
And disbanding the Iraqi army was both a formality--because it disintegrated during the invasion (at our urging, in fact, to avoid the legal responsibility of taking care of POWs that would slow down the invasion)--and necessary as the tool of the Baath Party to control and abuse the Kurds and Shia Arabs.
So the two biggest mistakes were not even mistakes. I can't believe that I still have to address these ridiculous claims so long after the war.
You know who made the biggest mistake of the Iraq War? Saddam Hussein. He believed in 2003 that American ground forces would never dare enter Baghdad out of fear of casualties and that eventually we'd withdraw, leaving his goons the chance to return to southern Iraq to kill any Shia Arabs who cooperated with the Americans and reimpose minority Sunni rule; and have the chance to cover his apparent bluff about having chemical weapons by defeating a half-hearted invasion attempt.
And as a result of that mistake, Saddam was chased from Baghdad, pulled from a hole months later, and years later tried and executed by his former victims. That was the biggest mistake of the Iraq War.
And you know what the second biggest mistake of the Iraq War was? Pulling American forces out of Iraq in 2011 and walking away from defending what we gained. That mistake was a better choice for cause of the Middle East that we struggle with (aside from the inconvenient fact that the post-World War II Middle East has been a roiling cauldron of war, oppression, and sectarian violence long before the Iraq War).
Recall that President Obama boasted of the stable Iraq we left behind when we left, Biden boasted Iraq would be one of the great achievements of the Obama administration, and President Obama's 2012 reelection campaign claimed that his victories in Iraq and Afghanistan allowed him to "responsibly end" our wars in the Middle East. Indeed, the entire premise of his "pivot" to Asia and the Pacific was premised on winning in the newly quiet Middle East. So at the time, everything in the region seemed pretty stable to the administration.
Don't tell me about mistakes when you can't remember what happened in the first place.