First reason, during a Water Fast you do not want anything but water, water is the most neutral thing that should go in your mouth. Most of other foods, enhanced waters and juices trigger digestive system to stay active. Although this has not been studied yet for H2O2.
Hydrogen peroxide has low molecular weight and the ability to destroy proteins, which facilitate diffusion through enamel and dentin. The dental pulp is where the blood vessels and nerves of each tooth reside, which makes this area particularly sensitive. A unique class of cells, called odontoblasts also reside in the periphery of the dental pulp area, which support the teeth by depositing new dentin layers throughout life and are also believed to play a protective/reparative role in response to dental carries or other environmental factors that harm teeth. The problem with hydrogen peroxide is that it has a cytotoxic effect on the dental pulp cells, which means that it literally kills them. A study published in 2013 in the Journal of Endodontics shows that even low concentrations of hydrogen peroxide trigger molecular mechanisms in pulp cells, which activate programmed cell death.