Question

Why does oxygen support combustion ?

Answer 1

To state that oxygen supports combustion it is an understatement. Combustion is an oxidation but a fast forward one. On the other hand an explosion is a fast forward combustion. Therefore, both of them are oxidations that release thermal and luminous energies.
FUEL OXYGEN AND HEAT ARE KEY REACTANTS IN THE PROCESS: COMBUSTION!
Oxygen supports combustion because by definition combustion is a reaction in which fuel reacts with oxygen or another oxidant. So oxygen is a key reactant in the process.