You just don't get it, fire's chemical reaction involves energy by default, but there are other types of energy that have nothing to do with fire. The energy we get from the digestion process has nothing to do with fire. Did you even read my last response, or choose to ignore it because that was more convenient?
And if fire was the only element that could create energy, would we get power from coal plants, hydro-electric plants, or wind farms? All fire does in those situations is release the energy stored in the kinetic energy other elements and help convert it into electrical energy that we use for our homes. The energy wasn't created by fire, it was simply used converted into electricity which would in this case fall under firebending despite electricity and fire being very different. But other forms of energy besides electric exist as well, such as my digestion example.
For instance, when an acid like vinegar combines with a base like baking soda, the chemical reaction create energy. Like digestion, that chemical reaction creates energy but is different from the chemical reaction that creates fire.
The bottom line. All energy is not fire, and therefore isn't classified as such. Period.