The explanation I saw was that radical oxides do a bit of damage to the cell and this triggers alarms which cause the cell to initiate repair mechanisms or kill

The explanation I saw was that radical oxides do a bit of damage to the cell and this triggers alarms which cause the cell to initiate repair mechanisms or kill itself. By taking anti-oxidants you are messing around with this alarm system, and basically make the cell live longer than expected, which increases cancer risk.