Well, the simple explanation is that combustion involves using
For example, if you burn methane completely, in open air:
#"CH"_4(g) + 2"O"_2(g) -> "CO"_2(g) + 2"H"_2"O"(g)#
And well, if you burn something, you're going to release heat into the atmosphere.
So, by definition, the reaction is exothermic, because it releases heat from the system (the reaction) out to the surroundings (the atmosphere).