Why does stabilizing something mean to move it to a lower potential energy? Why not to a lower kinetic energy?
I suspect it's because kinetic energy is relative. It's a product of the material's spacial relationship with other materials, rather than an inherent quality of the material. If am watching a molecule fly past at a million meters/second, that molecule has a lot of kinetic energy to me. If I'm moving along next to it at a million meters/second, it will appear to have no kinetic energy. But its potential energy will always look the same no matter where I'm watching it from.
What does it mean? Why is kinetic energy relative and potential energy not? You mean that kinetic energy depends upon the chosen frame of reference?
to start with, if chemistry was not such a joke perhaps one day the field will progress in a true form to represent biological frames. Stablizing to a lower potential could be considered a form of slowing down the resonance/vibrational energy. Such that to have a piece of iron cold is slowing it down from a hot (highly resonant state).... kinetic is like throwing a rock; momentum potential can be heat, to diatomic to even nuclear if you want to get technical but in the molecular form in chemical use, think in wavelengths, and you will run right on past your professor! see brownian motion to give you an idea of the observation process; it helped einstein perhaps you too ie.... to follow the path shared think of the energy as em (electromagnetic energy/Light) rather than ions or positve and negative charges, as that is the reason the chemists are lost in empty space.