Why choose trained than taught? (PTE)

1. Speed vs Rate:

The questions come down to, which one is correct: "technological change speed" or "technological change rate". Based on Oxford dictionary, rate means:

A measure, quantity, or frequency, typically one measured against another quantity or measure.

The text compares current technological improvement speed to the historical speed. Because there is a comparison (of speed), "rate" is more relevant than "speed".

You can also check some examples in this question, like:

You use "economic growth rate" not "economic growth speed" when it is expressed in a percentage.

2. Trained vs Taught:

Based on this answer:

Usage of the second object differs:

You teach a soccer player an individual skill.

You train a soccer player in a skill. (You can't train someone a skill)

it should be "trained" in this text because there is an "in" after the blanked-out word.