Hydrogen peroxide, as you’re probaly aware, kills bacteria. It will also kill fungus, and both are necessary to break down organic nutrients into usable forms for plants. Organic growing depends on a healthy population of microorganisms. Without them your soil is just dirt. If you’re growing organically, don’t use hydrogen peroxide.
Organic growing means using only organicaly derived nutrients and otherwise natural products and materials, as opposed to chemically manufactured fertilizers, and other products like Hydrogen peroxide. The medium can be dirt, peat, coir, etc. as long as any amendments meet organic criteria. As was said optimal organic growing is as much about growing good soil as it is about growing good plants, when the soil is happy the plants are.