The main complaint leveled against the game was that it would cheapen the sacrifices of the Marines who died in the Battle of Fallujah, and that Atomic Games would not depict the battle in an appropriately respectful fashion. This complaint got significantly louder after a developer implied that real, live Iraqi insurgents had been consulted during the development process.
Overall, I think it's pretty unfortunate that the title got nixed by controversy. Wars have been the subject of video games for as long as there have been video games. World War II games are still top-sellers, and for the most part their treatments of the conflicts in question are no more respectful or disrespectful than "Six Days in Fallujah"'s likely would have been. As for consulting with the insurgents, even games about World War II have crossed over and depicted the other side's viewpoint in the conflict -- Relic's "Company of Heroes: Opposing Fronts" put players in control of soldiers fighting for Nazi Germany as part of the single player campaign, and depicted some of those soldiers sympathetically.
The film industry has definitely delved into the Iraq War for dramatic material with movies like "Lions for Lambs" and "In The Valley of Elah," and HBO's "Generation Kill" followed a marine recon company in the early days of the conflict. Although those films were, for the most part, box office flops and received mixed reviews, there was very little suggestion that they shouldn't have been made at all. There's no reason why games should be treated any differently.