The pyridine/benzene stability 'paradox'?
When you think about stability, think of it as a relative value, meaning in comparison to atoms of other elements. Therefore, pyridine is more stable than the benzene but less stable than other elements, in general.

You are correct when you say stability is inversely proportional to reactivity. But because stability is relative, it is very difficult to comment on the relative reactivity.

EDIT

Heat of hydrogenation of an alkene in which the double bonds are conjugated is not additive because such an alkene is resonance stabilized, and, therefore, its Lewis structure, which the calculation would be based on, is a poor representation of the molecule.

I have found 2 aspects :


Pyridine is less reactive, than benzene toward electrophilic aromatic
substitution, because nitrogen is more electronegative, than carbon and acts like an
electron withdrawing group. As a result, the meta hydrogen is substituted.
Pyridine is more reactive than benzene because the presence of nitrogen
enables pyridine to react with nucleophiles. Nitrogen is an electron withdrawing
substituents enables the aromatic ring to participate in such reactions and the
substitution happens in the ortho and meta positions.