See
this paper.
Essentially, you need a chain reaction. One type of antioxidant donates an electron to a free radical, and that makes the free radical less reactive.
The antioxidant is now reactive itself, and needs a donated electron from another antioxidant, and so on, each time becoming less reactive.
But if you get a whole bunch of the
same antioxidant from a supplement or a "super food", this doesn't happen - so the antioxidants themselves become reactive, which is the exact opposite reason people take them.
But worse, free radicals send a "signal" to a cell to create it's own antioxidants...and if you're swarming with too many you've got from elsewhere, this never happens. Your body doesn't produce it's own antioxidants, which both prevents this same reaction happening, and also negates any benefit of exercise.
Or in a nutshell, the body is complicated - you need to get the balances right, you can't just throw stuff at it and hope it gets enough of everything.