1) People aren't dying of other stuff. Stuff that used to cause massive amounts of death just isn't as likely anymore. Infections are now routinely cured with antibiotics. Vaccines prevent deadly disease. Hygiene and health and safety standards across the board reduce death from other causes dramatically - there has been an increase in laws regarding health and safety in every facet of life.

People are living longer. The older you are the more likely you are to have cancer. It is hypothesized that given enough time everyone develops some kind of cancer even if microscopic (more on that later)

Automobile fatalities (the thing most likely to kill young adults) are down dramatically. This is due to safer cars and a decrease of things like DUIs due to public awareness and a huge increase in prosecution. My grandpa told me in the 70s police would routinely pull him over, see he was drunk, and tell him just to go home. New safety features are required almost every year on automobiles. People take infant car seats very seriously nowadays. When I was a kid as soon as I could sit upright by myself I was out of the car seat.

2)There's not a lot we don't know about cancer still. We know that it is a combination of genes and environment that cause it and there are things you can do to lessen your likelihood of getting it such as not smoking... but overall we haven't done a whole lot to prevent most types of cancer and still have a lot to go in completely understanding it. Which specific genes and which specific environmental factors are still somewhat of a mystery, I mean we know some stuff but still not enough. Some types like cervical cancer are largely (but not completely) preventable with routine pap tests but that's the exception.

3) Increased screening leads to an increase in detection of benign and asymptomatic cancer. This turns people into cancer patients who wouldn't have otherwise been cancer patients without screening. This is kinda a new thing. We used to believe that cancer runs one course - that it started at stage 1 and grew continuously until it spread all over your body and killed you - so catching cancer while it is small and treatable will prevent it from spreading and becoming deadly. We are learning from experience that isn't always the case, some can develop so slowly that there's no way it will cause problems in your lifetime. Take prostate cancer for example - the PSA test is a blood test that was developed to detect asymptomatic prostate cancer. The PSA test is no longer recommended because it lead to an increase in cancer diagnoses but a very modest corresponding decrease in cancer related deaths. That tells us that some men who would be diagnosed with prostate cancer if they had the PSA test wouldn't ever be diagnosed without it. Routine mammograms have detected thousands more very early stage cancer (Ductal Carcinoma In Situ) than ever before. The numbers tell us some of these new diagnoses wouldn't have progressed (and maybe would have regressed). Everything requires treatment though because we don't know which small tumor will become deadly and which one won't. More info on this is here:
http://www.newyorker.com/magazine/2015/05/11/overkill-atul-g...

>we’ve assumed, he says, that cancers are all like rabbits that you want to catch before they escape the barnyard pen. But some are more like birds—the most aggressive cancers have already taken flight before you can discover them, which is why some people still die from cancer, despite early detection. And lots are more like turtles. They aren’t going anywhere. Removing them won’t make any difference.

>Over the past two decades, we’ve tripled the number of thyroid cancers we detect and remove in the United States, but we haven’t reduced the death rate at all. In South Korea, widespread ultrasound screening has led to a fifteen-fold increase in detection of small thyroid cancers. Thyroid cancer is now the No. 1 cancer diagnosed and treated in that country. But, as Welch points out, the death rate hasn’t dropped one iota there, either. (Meanwhile, the number of people with permanent complications from thyroid surgery has skyrocketed.) It’s all over-diagnosis. We’re just catching turtles.

The other thing is you may just be hearing about it more or it might just be talked about more than it used to be.