Ok the actual answer is that H2O2 has a weak O-O single bond, plus it can react to form water – a very stable substance. So a low barrier to reaction plus a big increase in stability after it has reacted.
The danger is more from the fact that cells and tissues contain lots of delicate stuff like cell membranes. Oxidation of any chemical changes it’s properties, and something so specialised like a cell will likely not function afterwards. The human liver is effectively a giant oxidising machine, and historically scientists have used dried and ground-up pig liver to do some pretty amazing reactions.
H2O2 is very useful in the chemical industry, and is common in cleaning solutions and hair dyes.
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