Landing legs are the obvious way to recover a booster, and for a vehicle the size of a Falcon 9 they are the right answer. They stop being the right answer as the vehicle grows. Legs strong enough to absorb the touchdown of a 70-metre, largely-empty steel booster are heavy, and every kilogram of leg is a kilogram that has to be carried uphill and then decelerated again on the way down. They also have to be inspected, and they put the vehicle on the ground somewhere that is not the launch mount — which means a crane, a transporter, and days of turnaround.
Catching moves all of that mass and complexity to the ground, where mass is free. The tower arms are already there to stack the vehicle; if they can also catch it, the booster keeps nothing but two small load-bearing pins, and it ends the flight hanging next to the mount it launched from. That is the entire argument. It is not a stunt — it is a mass-budget decision that happens to look spectacular.
The arms do not close around the booster like a fist, and they do not grab the engine section. Two hard points near the top of the vehicle — small protruding pins, one on each side — come to rest on rails running along the inner faces of the arms. The vehicle is caught under the pins, from below, and then simply hangs. Almost the entire mass of the booster is beneath the contact point, which is what makes the configuration stable: a hanging object wants to align itself vertically.
This is also why the geometry is so unforgiving. The pins are a fixed distance apart, and the gap between the rails is only slightly wider. The vehicle has to arrive inside a window measured in centimetres of lateral offset and fractions of a degree of tilt. The arms can move — they track the descent and close at the last moment — but they cannot rescue an approach that is badly off.
In the simulator this is enforced rather than assumed. The catch check tests lateral offset, vertical rate and how upright the vehicle is at the moment the arms begin to close; a hull-to-arm clearance test runs on every build and fails if any part of the vehicle passes within 0.8 m of an arm during the close. If the sim tells you the catch was clean, the geometry was clean.
The booster separates about 70 km up, still moving downrange at several times the speed of sound. Everything after that is about reversing that motion and arriving with almost none of it left.
The upper stage returns from orbital velocity, which means it arrives with vastly more energy to dissipate and a heat shield doing most of the work. It also flies a completely different terminal profile.
Where the booster comes down engines-first and vertical the whole way, the ship falls belly-down — flat to the airflow, using its own body as the brake, with four flaps making attitude corrections. This is enormously effective: a vehicle in that attitude sheds nearly all of its horizontal velocity aerodynamically and ends up descending almost vertically, close to overhead of its landing point, at a fraction of terminal velocity.
Then it has to stop being an aircraft and become a rocket again. Engines light, the vehicle rotates from horizontal to vertical in a couple of seconds, and the landing burn arrests what is left. That manoeuvre — the flip — is the least forgiving few seconds in the flight, because it must complete with enough altitude left to null the descent rate but not so much that the vehicle is left hovering.
The simulator models the whole chain: the belly-down deceleration, a banked turn that walks the vehicle onto the tower's back side, the flip nearly overhead, and a final approach that crosses above the tower and settles vertically into the arms. The engine count steps down 3 → 2 → 1 as the margin shrinks, so the catch itself happens on a single engine.
You do not fly the vehicle. The interesting decisions are earlier and colder than that, and they are mostly about whether to commit hardware.
The honest summary of the job: a divert is not a failure, and the correct scrub is a good day. Read the boards, weigh the margins, and do not spend a tower to save face.
The Flight Manual covers the countdown and the polls in order; the glossary defines the vocabulary. Or skip the reading and fly one.