I don't know if you can dismiss a theory of what is possible in the universe because you encounter a paradox. Paradoxes say more about the limits of human comprehension than they do about the reality of the universe. Much of quantum physics involves what we perceive as a paradox and yet there it is - the most successful theory ever devised. In fact, quantum theory provides a possible escape from the causality paradox of FTL travel with its many-worlds interpretation. The MWI gets into the whole parallel univeres thing and I really don't want to try to describe it here. (Google it for an explanation.) It's an interpretation that is being taken seriously by many physicists, though. My point is that too many basic assumptions about our universe are still unresolved and so things like FTL really can't be ruled out.

When my father had lung cancer, I did a lot of research on cancer treatments and came to believe that the best possible treatment for cancer was to get the body's immune system to attack it. Especially for cancer that has spread, you need a systemic treatment that targets the cancer cells while not damaging the healthy ones and nothing will ever be as effective at doing that as the body's own immune system. This treatment is very encouraging and is on the right track. There are also several cancer vaccines under development that train the immune system to fight cancer before it takes hold. In the future, you may be able to get vaccinated against the kind of cancers that you are genetically vulnerable to.