A returning rocket has to land on legs; you cannot catch one out of the sky
The old claim turned out to be wrong and was rejected by evidence.
TaughtReusable rockets land the way SpaceX's Falcon 9 does, deploying legs and setting down on a pad or a drone ship. The idea of a skyscraper-sized booster steering itself back and being plucked out of mid-air by the launch tower is a rendering, not something anyone has done.
NowOn 13 October 2024, on the fifth Starship test flight, SpaceX's Super Heavy booster flew itself back to the launch tower and was caught in mid-descent by two giant mechanical arms, the 'chopsticks', on the first attempt. No booster had ever been recovered that way before.
What actually happened
The booster is about 70 metres tall and returned from the edge of space, slowing to a near-hover and sliding sideways to line up between the tower arms, which then closed around it before its engines cut. Catching it rather than landing it on legs is the point: it removes the weight of landing gear and, in principle, lets the same booster be re-stacked and flown again quickly.
The caveat worth stating: this is a test program, not routine operations, and later flights had mixed results. But the specific 'that can't be done', returning a booster of this size to its launch mount and catching it out of the air, was done, cleanly, the first time it was tried.
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Who was taught this
Still standard through 2024, so anyone who finished school between 1950 and 2024 learned the earlier version.