Free radicals and reactive oxygen species (ROS) in particular play an important part in aging because they direct repair and regeneration and taking antioxidants ruins this endogenous signal. Free radicals are (usually small) molecules lacking an electron needed for stability; they will steal an electron from the first thing they bump into. Like pulling a cog out from clockwork, stealing an electron from a protein or enzyme is usually not good for the finely-tuned biochemical machinery of our cells. The free radical might be rendered safe in the process, but it has left some form of chaos and damage in its wake.
Free radicals are sufficiently dangerous to biochemical machinery that some of our body’s defenders use bursts of free radicals as a kill mechanism. That is why Denham’s belief has died too slowly. Science changes though as data comes in.