Simply, it is an electron exchange rather than repel. Reduction-oxygenation - redox cycling. Oxidation describes the loss of electrons / hydrogen OR gain of oxygen / increase in oxidation state by a molecule, atom or ion.
It depends upon the antioxidant. For example, ascorbic acid (vitamin C) is a reducing agent and can reduce and thereby neutralize reactive oxygen species such as hydrogen peroxide.
Another powerful antioxidant, melatonin, once oxidized, cannot be reduced to its former state because it forms several stable end-products upon reacting with free radicals.