Who controls a rocket?

A launch vehicle accelerates too fast for a human being to steer it. From the moment the clamps release, the guidance, navigation, and control system compares the position and attitude measured by gyroscopes, accelerometers, and GPS against the programmed trajectory, and commands the engines to tilt a few degrees on their gimbals to correct course. The cycle repeats dozens of times per second. The entire sequence, engine ignitions, stage separation, shutdown, and payload deployment, is loaded in advance and the rocket executes it on its own.

The countdown is run by a launch director, responsible for giving or pulling the "go." Around them, in the control room, each console follows a subsystem: propulsion, pressurization, electrical, weather, telemetry. Anyone can call a hold if their parameter goes out of limits. In the seconds before liftoff, the decision passes to the pad computer, which aborts automatically if an engine fails to reach the expected thrust.

Separate from the launch vehicle team, the range (Cape Canaveral, Vandenberg, Kourou) keeps a flight safety officer with authority to activate the flight termination system if the rocket threatens populated areas. The newest launch vehicles carry that system autonomously on board.

On a crewed spacecraft, the crew monitors; they don't pilot. Their job is to interpret alarms and, if necessary, activate the escape system or a manual abort. The Soyuz and the Space Shuttle had limited manual modes; on the Dragon and Orion capsules, almost everything is done from touchscreens or from mission control, and ascent is fully automatic.