hm.. anitoxidant is not the opposite of oxygen. Antioxidants "cancel" out toxins, and free radicals. Antioxidants are vitamins such as E, A, minerals such a selenium etc. Oxygen that you drop into you drinking water is just pure oxygen, it is already present in our body. Lack of oxygen lead to an acid state, and acidity lead to toxins and free radicals. Oxygen actually helps the cells to get rid of toxins and oxygen is a great detoxing agent in that sense. It is all about helping our poor cells in there to their job, if they don't we get sick.
It is just oxygen, that is already present in our bodies, but you add some more do speed up the machinery :)
That's why adding oxygen to your drinking water is great.
And by that I mean oxydrops, for example