Cancer is adaptative in the same way. Tumors are populations of cells with variation (forget the part where your teachers said tumors are composed of clones, that's garbage). When you apply a selection, a small number of the cancer cells survive. Usually there are several different subpopulations. Then they grow, you end up with tumors that are mixed populations of different subtypes. Then the cells start growing again.

Saying cancer is just a failure mode of biology isn't given cancer enough credit. It's more like cancer is a side effect of complex organisms, which is nearly impossible to eliminate, without also eliminating a number of highly advantageous features of cells.