>>2006404>>cadenceGood points have been made already but i want to add the idea of staying on top of the gear you're in.
It's ok to mash a big gear slowly, but you have to be strong doing it. Straining at a gear, when your muscles are not firing, is extremely bad for your joints, and will cause injuries. So if you're in that big gear, if you are mashing, you have to be actually putting the power there. If you're riding a big gear, it's like the gear is pushing against you, and you have to be the one pushing harder.
One reason to ride a high cadence is that riding a high cadence is like chasing to be infront of the gear you're in, not pushing against it. If you spun fast enough, you would actually get in front of the pawls that engage the freehub, and could generate infinite power with zero resistance on the pedals. So trying to spin fast is going to protect you from getting behind the gear you're riding, and being hurt by the failed effort.