Anglo-Saxon culture, like many others, associated women with the evil arts. We can see this in the examples from Scriftboc quoted here. You can learn a lot about the connection between women and illicit knowledge by reading the essays on witchcraft in a photocopied pamphlet on Reserve in the Library, "Magic and Popular Superstition in Anglo-Saxon England," edited by D. G. Scragg. The essay by Audrey Meaney is particularly helpful.
The larger implications of this question might be more interesting than technical issues, but you should start with looking into definitions:
Meaney says it is a term for humans with supernatural powers, more often for women than for men. Witches are thought to do harm by means not available to others, but it is not clear that this is what the witch meant in Anglo-Saxon England. The witch could also be a healer or a prophet, and was usually a witch at birth.
The definition is important because witches are a threat to traditional power structures. That is, the witch has powers "normally" assigned to orthodox offices of power largely (but not exclusively) reserved for men. The status of "witch" (a stigma, rather) is a way to signal that certain powers, when held by women, are dangerous and evil.
It is particularly striking that so many words for "witch" in Old English are related to traditional sacred roles, including the prophet or seer. Note that when Kieckhefer brings up the witch (near the end of his book--see Bibliography), he focuses on later medieval evidence. The work of Christine Fell as well as Meaney will help you learn more about the Anglo-Saxon evidence.
If you are taking Old English, you can pursue this link as an exercise in word study.
Christine Fell takes up four key words and offices in the chapter on "Myth and Legend" in Women in Anglo-Saxon England; for more detailed discussion, see Audrey Meaney's essay on "Women, Witchcraft, and Magic" on reserve (in Scragg, Superstition and Popular Medicine).
These words are "wælcyrige," which is the root of Walkyrie or woman warrior; wicce; hægtesse; and burgrune.
We will look at two words using "rune." First is the "leodrune," is a "female skilled in the mysteries of a people" ("leod" means people); second is the "burgrune" ("burg" means fortified settlement, town), and probably refers to a temple priestess of some kind, perhaps a versions of the Furies of classical literature. In Beowulf Grendel's mother might be numbered among the "helrunan" (line 163, monsters, male and female) who live in the fens, with "rune" again indicating a supernatural being.
In Scriftboc the words for magic are "drycræft" and "galdorcræft," and "woman" rather than one of the specialized terms above is used to indicate the one who performs magic. "Wicce" is another word for witch that like others is connected to a sacred office, possibly prophecy. But "wicce" is not used in Scriftboc and is a complex term. Meaney suggests (18) that when Ælfric uses "drycraeft" he indicates a male actor and "wiccecræft" a female actor, but the Scriftboc seems to contradict this conclusion.
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