I have learned about electric permittivity in two contexts:

1. How much a medium reduces the strength of the electric field (Like if I have a charged ball inside a vat of oil, the oil will polarize and create its own electric field in the opposite direction that reduces the strength of the net field)
2. How high capacitance is in a parallel plate capacitor ($C$=electric permittivity of the dielectric in between the plates \* area of the plates / distance between the plates)

However, I feel like these two definitions are contradictory. In the capacitance context, I learned that the less polarizable something is, the better an insulator it is, and therefore it has a greater electric permittivity because electrons have a harder time jumping between plates so the plates can be more charged per volt (At least that's how it was explained to me - it might have been a simplification). So in this definition, less polarizable substances have higher permittivities.

But in the context about electric field, it would make sense to me that more polarizable substances have higher permittivities. My logic is that the more polarizable something can be, the greater an opposing electric field it can create when polarized (For example, Argon gas would diminish the field strength greater than Helium gas because each molecule has more electrons so they have a greater degree of polarization - like in London Dispersion Forces).

My understanding leads to one definition saying that less polarizable substances have higher permittivity and the other definition saying the opposite. Where is my mistake?