You have to either be a witch or a warlock in order to fly a broom. Broom flying takes magic, which humans do not usually have (or have enough of). The best chance you have of riding a broomstick is by meeting a witch/warlock.
Another perspective:
Broom riding has been around for a long time. There are rites and festivals that involve people riding on a broom, such as at Beltane (May 1st) where couples and individuals may ride a broom between 2 bonfires to have a blessed year and to bring good luck. This huge misconception of actual flight comes from the astral projection, hedge riding, and other methods cunning folk and modern day witches use to obtain information from the Akashic Records, or the collective consciousness of the planet. These methods are also used to commune with spirits on occasion as well.
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