There are some heritable cancers e.g. retinoblastoma, look up Al Knudson's two-hit hypothesis. Or the BRCA genes. In those cases, where all cells have the mutation, yes indeed cancer is hard to defeat. This is why Angelina Jolie had her breasts removed and replaced, she carried the BRCA allele.

In more common cancer types, cancer is the result of cumulative mutations over a lifetime. Sequences of mutations occurring one after the other, over years, until it reaches the cancer breaking point. So to cure these patients means removing those cells with those mutations, a subset of all cells. To not cure, means some cells remained. Cells can be destroyed with surgery (removal), radiation, chemotherapy, immunotherapy (which stimulates the immune system to destroy them, elegant)

Now, there is also the concept of field cancerization, if a tumor is removed, neighboring cells have SOME of the mutations seen in the cancer, just not enough to be themselves cancer, having to do with this lifelong process of sequential cancer mutations. This is a serious topic among cancer surgeons - how much should I remove? Should I remove extra for fear of field cancerization?

Keep in mind, the standard line is that all cells in our body have the exact same genome, in truth that is not the case (as cancer shows us) and recent articles in top journals in the past year have implicated that even our non-cancer cells carry slightly different genetic variation, thought to be mutations in the first month or two in utero. This was done by correlating mutations found only in specific tissue types with the embryonic origin of those tissues. As such we can say our cells our all 99.99999% the same DNA sequence as each other, but there are small differences and major subpopulations.