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Burning is called an oxidation-reduction reaction that creates a very high enthalpy change. A compound is oxidized (with another oxidizing atom / compound) into its much less energetic form. In other words, in order to create a burning reaction, we need a "high electronegativity" atom with high oxidation power (which can reduce itself), that is, a very good electron acceptor.
These high electronegative atoms that we have to choose to produce a possible burning will be either halogens (i.e. you can "burn" something using fluorine) or oxygen. In fact, peroxides such as Hydrogen Peroxide are similar oxidizers, CH4 (methane), which is a simple carbon compound, is oxidized with hydrogen peroxide and converted to carbon dioxide and water, as well as oxygen, and converted to the same compounds and burned.