Why is DNA replication not 100% accurate
Nothing is 100% precise - any measurement or process allow for some error, the only difference is how often such errors occur (i.e., the probability of an error). These wildely range in biology - e.g., it is about 1 per $10^4$ in HIV replication, but only 1 per $10^9$ for human DNA (due to the repair mechanisms).
Note that $1$ in $10^9$ for human DNA means pretty much that there is about 1 error per each copying of the genome (which has the size of about $3\times10^9$). One could therefore still pose a question of why the error rate is so high? E.g., Human body consists of about $15\times10^{12}$ cells. Thus, if the error rate were about 1 per $10^{22}$($\approx 3\times10^9$ by $15\times10^{12}$), we could have human organisms consisting of the cells with identical DNA.
The answer to this is that errors are not necessarily bad: the copying errors are the source of the mutations driving the evolution! Note also that many of the errors have no effect at all on the well-being of the organism. Thus, it is fair to say that the existing error rates were selected by the evolution for assuring the appropriate rate of the evolutionary change/adaptation, without causing immediate harm to the organism. (One could even speculate that 1 error per genome copy is the appropriate rate across the organisms, but for a moment I cannot support this assertion by references).