I assume you meant DNA.
But it doesn't share the same DNA, and that's the point. DNA is altered all the time with retroviruses that are inherited. As cells reproduce through your lifetime, mutations do happen, and they sometimes produce cancer. Every time a cell divides, a little more of the DNA strand is cut off at the telomeres (which exist merely to absorb the truncation) and eventually this can expose viable DNA structures to mutation.
I could go on, but other things are pressing....
Thus the cancer cell is a failed mutation?