Since copying is very very slightly imperfect, just about every cell division is likely to produce an error. We go from one cell to x trillion, which is on the order of thirty-plus cell divisions; every single cell in your body has a statistical chance to be unique in some one-part-per-billion way, not *exactly* like any other cell.
Human DNA consists of about three billion “codons” – one of the letters C A G T. The other side of the double helix has a different codon, but they only occur in pairs. So consider that a three billion digit number in base 4. This equates to 675 million 8-bit characters, or about 900 million alpha characters (they take 6 bits each).
That’s a book of 150 million words (average word size in English is five letters, plus a space or punctuation.)
Now imagine a 150 million word book with one or two typos.
Look close – DNA copy errors are repairable in a healthy individual, but of course that’s not foolproof. And radioctivity, free radicals, cosmic rays, etc. cause additional errors.
Unstoppable? That’s certainly one way to put it. Genetic mutations are the norm, even though each one is like one typo in a thousand fairly long (150 thousand words) novels. A decent novel these days runs to 75 thousand words; one book from Game of Thrones runs more like 250 to 300 thousand.
Startling when you see it up close – on the one hand, THERE IS NO WAY TO “STOP” MUTATIONS, and on the other hand IT TAKES A LOT OF TYPOS TO MAKE A REAL DIFFERENCE.