I know that we see in experiments (physical and thought) that energy is always transformed into something else, but what propels our universe to behave this way? What is happening at small levels that only allows conservation as a possible outcome and not destruction of energy?
Update: Based on a given answer stating that energy is mass, I should probably then expand this question into "Why must mass must always be conserved?"
The answer saying that energy was mass was incorrect. And neither is conserved, and neither is even additive.
In General Relativity you have a Stress-Energy energy tensor. It has ten independent components in any frame. And you can try to extract one of them to be the energy density and three others to give you the components of the momentum density. But that decomposition is locally frame dependent. And even if you did that, you only get a density at every point and since a surface of simultaneity depends on a global frame (which don't always exist and aren't unique when they do exist) trying to add up those densities at different points on a surface of "same time" to get a total energy and a total momentum is hopeless generally.
So there isn't an energy of the universe. And there isn't a momentum of the universe. And even if there were, they could be infinite. And even if it when they are finite, then the mass would satisfy $$(mc^2)^2=E^2-(\vec p c)^2$$ and the mass of the universe would not equal the sum of the masses of the parts. And since the energy and momentum would change over time, the mass usually changes over time.
