I kept looking to see if I am eating something wrong. So can someone with better understanding of antioxidants explain if this is only via vitamin or if it's specifically present in some types of food.
If I were to speculate it might be that while normal cells can make enough for themselves cancerous cells benefit from external antioxidants. The damage done by free radicals is mostly concentrated in the mitochondrial genome, which is why evolution has brought as many genes as possible out of the mitochondria into the nucleus. By contrast the mutations that causes cancer are, IIRC, mostly inside the nucleus.
I highly recommend it if you don't mind the higher degree of technical content than your average popularizing science book
I don't know about this article specifically, but the importance of hormesis in medicine has come on fairly strongly in recent years. Specifically, that persistent, low-level damage to your cells and subsequent autophagy can actually reduce one's risk of various ailments. Antioxidants reduce the occurrence of this damage.
I'm not a medical professional, but I think whole, healthy foods are generally good choices.