The distance between first and second base is 90 feet which is shortened by 5-6 feet for most base runners trying to steal second with their leadoff. If a catcher stood at home plate with ball in hand when the runner took off, it would only take a 35-mph fastball thrown to second to get the runner out.
However, begin the sequence with the pitcher holding the ball and throwing a 90-mph fastball directly to the catcher's mitt. If the runner took off at the precise instant that the pitcher released the ball, the catcher would need to receive the perfectly thrown ball, stand up, cock his arm and throw a 60-mph fastball to second base to get the runner out.
Now, put a batter into the equation. Add a pitched ball that was NOT perfectly thrown to the catcher's mitt (the target) and toss in something other than a nice crisp 90-mph fastball -- something like an 85-mph curveball or slider. The catcher now has to receive this ball under game conditions, stand up, position himself to avoid the batter (sometimes made worse by left-handed batters) and throw a fastball 85-mph to second base to get the runner out.
A pitcher, standing 60'6" away from homeplate, has plenty of time to get set, to concentrate, to wind-up, and to throw to a target some 17" wide and 36" high. There is plenty of time to get the grip just right on the ball and to "mentally" control his mechanics of his throw. A catcher, on the other hand, has to throw a distance of approximately 127'3" to a target that is "framed" by the shortstop's (or secondbasemen's) glove poised over a base by inches rendering the target 9" wide by 18"-20" high. This target is 1/4 that of the strike zone. The catcher has to do this without the benefit of a casual, well-thought out preparation and a "just so" grip on the ball.
That makes a catcher have to do twice as good as a pitcher just to get a "passing grade".