Failure is more of a nervous system event than a muscular one -- the nervous system (which causes the muscles to contract via signals from the brain) cuts you off before the muscles are truly 'done'. The real problem with going to failure with regularity is that the nervous system takes longer to recover than the muscles. You can train much more frequently (i.e. squattng 2-3x/week instead of once) by doing more sets short of failure. More frequency = more workload = more stimulus.
I wouldn't say that one should never go to failure, but to do so at nearly every workout is counterproductive. I almost never squat less than twice per week, and I use heavy weight and decent volume. I have made the best gains of my life by avoiding failure for the most part (unless really pushing for a PR or something) and relying on constant, incremental improvements on the big lifts.
Failure is less detrimental on smaller lifts by nature, as there is far less nervous sytem activity involved in a curl than a deadlift or squat.