Even worse, it is frequently explained with an analogy to escape velocity. You have a certain escape velocity at the surface of the Moon, the analogy starts, and your rocket needs to exceed that to get out. Gravity is stronger at the surface of Earth, so escape velocity there is higher, and rockets need to go even faster.
At the event horizon, gravity is strong enough that escape velocity is the speed of light, and so nothing can get out because you can't go faster than light.
Great--except the escape velocity thing only applies to trying to get out ballistically. (Current rockets are essentially ballistic because they expend most of their fuel while still deep in Earth's gravity well).
Escape velocity explains why someone inside the event horizon can't throw things out of the black hole using a catapult, or using a rocket that expends all its fuel before reaching the event horizon.
It doesn't explain why something with continuous thrust could not get out. It doesn't explain why someone inside couldn't build a ladder that extends past the event horizon and simply climb out. It doesn't explain why someone outside could not lower a tether in and pull someone out.