With the benefit of hindsight, we now realize that in Metal Gear, Big Boss sent Solid Snake, his clone, to eliminate his own body double, Punished "Venom" Snake. He always viewed Venom as dispensable if not necessary to dispense with at some point, and, presumably, then seized control of the organization that he and Kaz built and integrated it into his own.
The United States sent Solid to take out Metal Gear, and to rescue an agent that had already attempted to infiltrate Outer Heaven. While this operation was lead by Big Boss, who had returned to the States to infiltrate the upper echelons of the special forces and intelligence communities in the United States, the intention wasn't to kill Venom. It was to ensure Venom had time to finish the Metal Gear weapon. Big Boss deliberately picked Solid due to his relative inexperience, hoping he'd fail.
The United States sent Solid to take out Metal Gear, and to rescue an agent that had already attempted to infiltrate Outer Heaven. While this operation was lead by Big Boss, who had returned to the States to infiltrate the upper echelons of the special forces and intelligence communities in the United States, the intention wasn't to kill Venom. It was to ensure Venom had time to finish the Metal Gear weapon. Big Boss deliberately picked Solid due to his relative inexperience, hoping he'd fail.