My understanding of the case against antioxidants is that thefree radicals (etc.) are an essential cell signaling mechanism ... and the signal is "kill me, I'm a bad cell".
If you somehow disrupt or eliminate the signal, you allow bad, or inefficient, or perhaps cancerous cells to live longer than they would otherwise.
I'm paraphrasing directly from the excellent, excellent book _Power, Sex, Suicide: Mitochondria and the Meaning of Life_ by Nick Lane, which is highly skeptical of antioxidant supplementation and is a truly fascinating book.