When the soil is dry, roots get much-needed oxygen. When watered, they get much-needed water. This is why clay pots, which are porous, make for much healthier roots. Putting peroxide in your plants' drinking water seems to me like an excellent way to ensure sufficient oxygen to the roots. If you're asking why plants don't just get oxygen naturally, you have to bear in mind that a potted plant is divorced from most of the natural processes.
Tap water contains less oxygen than rain water and probably contains chlorine.
For my potted plants outside, I keep buckets out to catch rain water. Add the peroxide just prior to watering. Must be important stuff. This does not surprise me, but it pleases me. See if you can find another site with as much information from such a wide variety of sources.