It may have been Superman, but the United States government proved that they were the Man of Steel's darkest threat of all. In the wake of a Kryptonian resurgence, a dark conspiracy revealed itself and it aimed to take down every Kryptonian, even Superman, for good.
As one of the DC Universe's most powerful heroes, Clark Kent has no short supply of villains who are ready to challenge him. Whether it's the ingenious machinations of Lex Luthor or interdimensional trickery of Mr. Mxyzptlk, Superman has gone up against some pretty devious foes. But it was the infamous villain Doomsday that killed Superman, cementing his place as one of the top enemies in the hero's rogues' gallery. Few enemies have been able to hurt the Man of Steel in the way that Doomsday did, though the sheer force with which the monster defeated Superman brought valuable insight into how the Kryptonian could be taken down.
Such information proved invaluable to a clandestine military operation aimed at ensuring that the Earth would be safe from any Kryptonian threat, even the beloved Superman. A deadly conspiracy was uncovered after the Bottle City of Kandor was revived after Geoff Johns and Gary Frank's and Supergirl's father, Zor-El.
The general may have had a point that the idea of thousands of unchecked Kryptonians roaming around on Earth is a slightly unsettling prospect. After all, just because they all shared the same powers doesn't mean they have the same moral center. But hints of Project 7734 were shown before Kandor was ever revived, indicating that the program was never for a swath of Kryptonians but just one—Superman.
As the most powerful being on the face of the Earth, Superman is always going to face detractors afraid of the notion of him turning evil. Even Batman has kryptonite to defeat Superman in case the nightmare scenario comes true. But few people in the DCU actively plan against Superman. Obviously Lex Luthor is resolute in his belief that Superman needs to die for the sake of humanity which makes it all the more alarming that his line of thinking was endorsed by an operative of the U.S. government. Superman has the best track record of heroism and has shown multiple times he's on the side of good, but the government apparently can't take that risk. The United States would rather work with a Doomsday they can control instead of trusting an independent Superman.