I have been studying torsion theories and it seems like some sources always mentions without justification that torsion theories are a successful formalization of localization within several mathematical fields as you can see here
https://ncatlab.org/nlab/show/torsion+theory#properties
in part 3. Some other books go further and say torsion theories formulate localization in other contexts like algebraic geometry or topology. Of course they don't explain why. But for being honest I don't see how this definition of a torsion theory is a formulation of localization in abelian categories. Can anybody explain me how this happens? So far it seems to me this is only a fake merchandise to study torsion theories.