You're confusing possible implication and necessary implication. The flu virus causes the flu. it is the only thing that causes the flu and it if called the flu virus because it causes the flu. That said, you can carry the flu virus in your body, and not have the flu.
In the case, Carcinogens cause cancer. They are called carcinogens because they cause cancer, but you can have carcinogens in your body and not get cancer. Does that make sense?
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