The reason we say mass and energy are the same thing is because how we distinguish them is just a matter of bookkeeping – which depends on our point of view. But if you think of heat as a form of energy rather than of mass, then it is indeed easier to convert mass to energy than vice versa.
When a chemical reaction reorganizes matter into a state of lower potential energy, such as for example whenever we burn a fuel, the energy released typically gets converted to kinetic energy and quickly distributed among many particles of a larger system in the form of what we call heat (which is impossible to fully recover in the form of usable work). An observer looking in detail at the system will see each molecule as having a tiny bit less mass than its component atoms (by an amount corresponding to the binding energy) with the total of all these differences also corresponding to the increased kinetic (heat) energy of the molecules.
On the other hand, when we break apart a chemical bond then we must provide some amount of energy and the resulting masses of the components will add up to that much more than the mass of the molecule. But if we want to do so in a consistent way (such as in electrolysis of H2O or carbon capture from CO2) then we need to provide the energy in a very specific way that is not so trivially easy to set up as just exposing fuel to oxygen.
However, if we measure the mass of the system as a whole (either gravitationally, or as inertia at starting from rest), then the result we get includes not just the masses of all its molecules but also their kinetic energies relative to its centre of mass. And that total (which includes all of the heat energy in the system) remains absolutely constant and never either increases or decreases.