What's more responsible for the increased incidence of cancer as we age?

Exposure and Damage. As we age, we are exposed to more environmental toxins and other causes of dna damage. The dna damage can cause development of cancer cells. Also, some cancers are very slow growing and may take years to become clinically obvious so they "appear" at later ages.
DNA damage. Cancer is the result of multiple insults and cumulative damage to the dna. Some damage may be inherited, but most is acquired through interactions with chemicals, radiation, infections and cell multiplication. With aging there is more exposure to cancer causing agents that damage the dna and many of the defects are cumulative resulting in increase in cancer with aging.