Well, P53 measures the level of DNA damage and other related factors in the cell and can cause cell death if the damage is bad enough, if the damage is not bad enough the P53 Protein could rather cause the cell to stop reproducing then death. The P53 protein has many functions and connects into many parts of the cellular metabolism using other proteins to measure these factors. Any mutation to P53 or its protein watchers could cause the P53 Damage defense pathway to fail and allow cancerous cells to form.
The reason for so much damage after cellular production is the fact that the cell has to copy nearly 3 billion in humans DNA bases, which is alot of data around 3 Gigabytes ruffly but this all has to be reproduced chemically which allows for many more mistakes than modern electronic data transmission. These proteins that copy the DNA have error rates, which is the rate that they make mistakes in copying the DNA, these DNA polymerases have a error rate of 1 in 100 million which 99% are fixed by Repair Pathway proteins, but sometimes the proteins of these repair pathways gain mutations and fail to repair the damage, when copying 3 billion DNA bases that is around 30 mistakes, which if not fixed has the possibility of 30 malfunctioning genes/proteins. This damage is normally very minor if 99% of them are repaired by DNA repair proteins which would mean 1 still remains after DNA repair. The mutation rate of reproduction of that much DNA is very small by the DNA polymerases, compared to RNA Polymerases which is about 1 in 5128, but still mistakes happen as the cell reproduces many times, but the amount of DNA copied is why Reproduction of the cell causes so many errors and failures of DNA Repair Pathways.