Within the shoving model of the glass transition, the relaxation time and the viscosity are related to the local cage rigidity. This approach can be extended down to the atomic-level in terms of the interatomic interaction, or potential of mean-force. We applied this approach to both real metallic glass-formers and model Lennard-Jones glasses. The main outcome of this analysis is that in metallic glasses the thermal expansion contribution is mostly independent of composition and is uncorrelated with the interatomic repulsion: as a consequence, the fragility increases upon increasing the interatomic repulsion steepness. In the Lennard-Jones glasses, the scenario is opposite: thermal expansion and interatomic repulsion contributions are strongly correlated, and the fragility decreases upon increasing the repulsion steepness. This framework allows one to tell apart systems where soft atoms make strong glasses from those where, instead, soft atoms make fragile glasses. Hence, it opens up the way for the rational, atomistic tuning of the fragility and viscosity of widely different glass-forming materials all the way from strong to fragile.