Fire is the rapid oxidation of a material. Water is 2 hydrogen and 1 oxygen. Every molecule is fully oxidized. It's also a common byproduct of fire. Therefore, you can't burn it, because it's already burnt
You call that an unstable compound that doesn’t want to exist. Hydrogen peroxide is constantly looking for an excuse to decompose back into water and oxygen. Making it is like rolling a barrel uphill. As soon as you let go, the barrel will roll back down to the bottom of the valley.