An important point – KaalBhairav Jayanti is also an occasion where, as an act of piety, we try to do something nice for a dog.
Often this entails feeding ; although if you are doing the full style thing, then in Nepal it is common to see dogs having had tilaka applied and garlanded with flowers.
Our family dog (who is healing from some rather worrisome injuries at present) has been getting some good attention (and enjoyed a bit more before I sat down to write this tonight), so all I can do to ‘do more’ for the occasion is ensure that a portion of my tonight’s worship and offerings are also done on his behalf.
Now as for why the Dog is to be looked after upon this observance:
The Vahana (steed) of Bhairava is a Dog, and there is a broad pattern of Shiva’s association with Dogs and Wolves (seen also viz. Odin having Freki & Geri); indeed, if we trace the archaic form of the myth that KaalBhairav Jayanti emanates from – it should come as no surprise that the God Himself appears in strongly Dog associated form.
The Star of Sirius is spoken of as the Hunter Who intercedes to protect the Goddess ; and likewise in Greek presentations this role turns into the hunting dog(s) that rip apart Actaeon due to the latter’s attempted interference with Artemis and/or Semele.
We may thus fairly say that we look after the Dog on KaalBhairav Jayanti because the Dog is not only ‘Man’s Best Friend’ – but the close associate, indeed an emissary an even form of a God as well.