It is in overdosing of the antioxidants that you find the problem. Moderation and balance is always needed. Our bodies need antioxidants or free radicals will take us down; we cannot live without antioxidants, so to say if you take antioxidants you will get cancer is absurd. We all take in antioxidants in one form or another, so logically everyone is at risk of cancer, and yes, everyone that dies of cancer were taking antioxidants - even a blueberry is an antioxidant.
What is important is to get your antioxidants from a natural source, like blueberries as an example; your body will know exactly what to do. It is moderation. We eat well, eliminate the chemicals and toxins [that we can control] and hopefully we have fed our bodies well enough to fight off pathogens.
If you have cancer already, a sharp change in diet and lifestyle will slow the cancer, giving you time to deal with the cause and attack it from several fronts with alternative treatments that work.