This article is inhumanly stupid. Does NO ONE here understand that oxidation doesn't refer to oxygen? It refers to an atom's / molecule's tendency to donate electrons to make bonds.
When it says that peroxide is oxidative, that means that it is reactive, aka it goes into your body and reacts with whatever is near it. It doesn't specifically target cancer or parasites or germs or anything else that is implied in this article. It works like free radicals and participates in reactions that shouldn't happen in a biological system.
in short, don't ingest hydrogen peroxide since it causes cancer