Why aren't resorcinol and catechol classified as dihydric alcohols?
As @Loong pointed out in his comment, resorcinol and catechol are phenols, not alcohols. Although both classes of compounds contain an O-H group, they are different in that the oxygen in phenols is bonded to an arene ring such as benzene or napthalene.
Importantly, a lone pair on the phenol oxygen is able to interact with the aromatic $\pi$ system via resonance, which gives phenols characteristically different properties to normal alcohols.

The lone pair delocalisation increases the electron density in the ring dramatically at the ortho and para positions, as indicated by the negative charge at these positions in the resonance structures. This makes these positions much more reactive towards electrophiles than they are in unsubstituted benzene.
The lone pair delocalisation also occurs in the phenoxide ion, the conjugate base of phenol, which makes it much more stable than a regular alkoxide ion, and therefore makes phenols much more acidic than alcohols.