Increasing cancer rates is an illustration of a statistical principle called "sampling without replacement".  If I pull all the clubs from a deck of cards, the odds of the next card you pull out being a spade or red card are going to be higher.  As the properties of the *entire* deck are altered, and nothing is put back, the odds change for what's left in the deck.

As time has gone on, more and more preventable sources of mortality have been systematically prevented through medical and often social advances.  But a person still has to die of SOMETHING.  The question that prompts is "What's left?".  And much like the cards in our example above, the odds of it being cancer (as opposed to scarlet fever, household fires, violent mobs, or malnutrition) go up.

That is not to dismiss concerns about carcinogens introduced to contemporary life (e.g., smoking, asbestos), but even in their absence, cancer rates would go up for the reasons noted above. We need to budget for that.