About NOT falling? What whiz said... I can't be said any better. There's no reason why a climber should expect a fall in their career. It's a dangerous job but it can be done safely... the climber has to have a certain combination of characteristics, patience being a big one, but totally doable.
I do think that it's pretty much inevitable that a climber will be injured at some point, your exposure is very high and there's all these sharp things working around soft things that matter a whole bunch and big heavy wood swinging around. Sooner or later something personal gets cut or mashed. Good on'ya to the guys who beat the odds... lady luck's never been all that good to me.
I fell with a tree that broke right at the root base, spiked in about 40', tagged the corner of a two story house on the way down. Pretty bad concussion, torn left MCL, fractured right tibia, totally screwed up my teeth, broke my nose, blablabla... it hurt, I don't recommend it.