The mythology about witches have remained for a long time. These myths do have a grounding in reality (even though we can’t really settle on whether witches are real or not). This brings us to the question- why are witches always depicted with broomsticks? Of all the things they could fly away on, a broomstick seems to be a rather odd device.
This is quite a NSFW tale, but one that is extremely interesting. From a modern view point, it is believed that witches were essentially women who were considered too knowledgeable or too forward for that particular age (and in some cases, people who were too old, and could not defend themselves against accusations). At that point, women were supposed to be domesticated, and remain at home, so professional women were not found too often. In this situation, a broomstick became something associated with the women- for they were the gender that was supposed to do all the domestic work.
However, there is another side to broomsticks– they are rather phallic in stature. Add this to the fact that they were used widely by women, the idea of “riding away on a broomstick” became an image that described women that did not follow the rigid gender, and sexual morality of the day and period. This is the reason why witches are always depicted to fly on broomsticks.