A lot of people want to know what a familiar is.
In the old days familiars were believed to be demons that take the form of an animal to help witches but witches were also believed to be ugly and ride brooms so we don't know if that's true.
Through time as people got more informed about witches they learned that familiars could be a pet that was or is very close too you or a spiritual animal that guides and/or helps you.
It's believed that a witches familiar if not a pet but a spirit or demon it tends to take the form of a cat.
I did some research and found this
'In European folklore and folk-belief of the Medieval and Early Modern periods, familiar spirits (sometimes referred to simply as "familiars" or "animal guides") were supernatural entities believed to assist witches and cunning folk in their practice of magic. According to the records of the time, they would appear in numerous guises, often as an animal, but also at times as a human or humanoid figure, and were described as "clearly defined, three-dimensional forms, vivid with color and animated with movement and sound" by those alleging to have come into contact with them, unlike later descriptions of ghosts with their "smoky, undefined form [s] ".
When they served witches, they were often thought to be malevolent, while when working for cunning-folk they were often thought of as benevolent (although there was some ambiguity in both cases). The former were often categorized as demons, while the latter were more commonly thought of and described as fairies. The main purpose of familiars is to serve the witch or young witch, providing protection for him/her as they come into their new powers.
Since the 20th century a number of magical practitioners, including adherents of the Neopagan religion of Wicca, have begun to utilize the concept of familiars, due to their association with older forms of magic. These contemporary practitioners utilize pets, wildlife or believe that invisible spirit versions of familiars act as magical aids'
So they need to be bound to a living animal? I read Nick Hall's book on egregores and thoughtforms, and it seems this is the same sort of thing. Some people call them serviotrs and demons can grant them to a magician to carry out his will. I guess they could be cat shaped, spirits and thoughtforms come in all different shapes. For people not big into religion, chaos magic has a lot on creating these entities.
The flying on brooms thing is related to hallucinogenic flying ointments and how they were often administered.
But familiars aren't and never have been pets, that's one of those pop culture things that a lot of people seem to have latched on to for some reason. IF your pet joins you when you're doing magic, that doesn't mean it's trying to help you, it means you're there and it wants to be close to you.