The stereotypical image of a fairy-tale witch involves cats, broomsticks, and boiling cauldrons. It’s thought this stereotype originates from the medieval ale-wife, also known as a brewess or brewster.
Brewing beer during the medieval period was often a women’s task. Women brewed on both a domestic and on a commercial scale. Brewing was a important job as it provided safe drinking water (which today we'd call ‘small beer’) using chemistry. It must have looked like magic!
When making beer the boil stage was done in a large steaming and bubbling metal pot over a fire. Lots of delicious malted grains are required which might attract vermin that a cat would be useful in combating. Any building had to display an ale-stake above the door if inside it beer was brewed. This was a stake with foliage and twigs wrapped about on end of it, a bit like a broomstick. Some of the bubbling and frothing vessels that turned sugary wort into a safe alcoholic liquid must have been seen as some kind of witchcraft or wizardry - especially as people didn’t know what yeast was at this point in history.
Source Jane Peyton Beer Sommelier, booze historian and author.