I've broken rigging ropes and slings under extreme loading situations, but a climbing line (even a slightly compromised one) has a near zero chance of breaking under normal conditions.
Every story you read about rope breakage, whether in rock or tree climbing, always has other mitigating factors. Dan Osman famously did a few free falls using ropes that had been left outside for a month in snow and rain. Ultimately, it was friction that cut his rope and led to his death.
The amount of force needed to break a modern synthetic rope is much greater than the human body is capable of withstanding. You'll break yourself before you break the rope.
BUT, there are exceptions to everything which is why we preach replacement.