[T01]

You're right!

Yes, this reasoning is fallacious. The key point here is that everyone eventually dies of something. The main reason that the death rate from cancer has increased in the past 40 years is improved treatment and prevention of other diseases, especially infectious diseases. This has led to increased life expectancy, and to an increase in the death rate from diseases which cannot be so successfully cured (especially in old people), such as various forms of cancer.