They are going up, but not if you take into account two factors. You should correct for age, because cancer goes up with age. That accounts for a lot of the increase, because every year life expectancy gets longer. We're the longest-lived people in human history and life expectancy is getting longer even faster. The second factor is smoking.
Smoking causes one-third of cancer, and that accounts for the major increase in cancer.
If you correct for age and correct for smoking, cancer rates are coming down. There's no evidence that's really convincing. It's almost all hype. Synthetic chemicals are just a drop in the bucket compared to natural chemicals. You make a thousand different chemicals when you roast your coffee.