Why do Mutations Occur in our DNA?

We always here about cell mutations that can lead to various ailments but how do these mutations actually occur when DNA is a perfect blueprint that is nearly impossible to circumvent? DNA like anything else is not impervious to damage. When a fragment of a gene becomes damaged through UV radiation, chemical disturbance or other means, the cell is usually able to repair itself correctly because nucleotides have complimentary base pairs that only fit together a certain way. The system is failsafe for the most part until a section of the double helix in your DNA breaks off completely on both ends. Now instead of being nearly impossible to fit a square peg in a round hole, the impossible becomes very possible as there is nothing to pair up to. The result, nucleotides will still only fit together a certain way but the order that the nucleotides appear may be changed. Since the sequence of nucleotides is critical for the blueprint of each species, the slightest mistake can have grave consequences. Usually this is bad for the individual but in extremely rare cases, that mutation will actually be beneficial leading to a survival advantage and a new species is born.