The concept of Christian Witchcraft is not accepted by all those who practice witchcraft. There is a school of thought that Christianity and witchcraft are too separate in belief and structure to ever be compatible. It is however important to note that Christianity is a religion and witchcraft the secular practice of magic so in theory the two are not in direct conflict. Where there would be a direct conflict is simultaneous adherence to the Christian and the Wiccan religions. A person cannot practice two religions at the same time. You may well come across Christians who practice magic or Wiccans who accept the teaching of Jesus Christ but there is and never could be such a thing as a Christian Wiccan.
There are some Christian witches who believe that the female deity, the Goddess, is represented in Christianity in the role of Mary, mother of Jesus. This belief would be consistent with the beliefs of those witches who do choose to work with divinity (and many of course do not) but would not be consistent with the Wiccan faith as Christianity is a monotheistic faith which specifically advocates the worship of a single God (going so far as to make the worship of other Gods a direct breach of the faith) and the fundamental premise of Wicca is honoring the dual deity.
Most of the arguments against the concept of the Christian witch are bound up with interpretations of the Biblical scripture in particular the verse from Exodus (22:18) "Thou shalt not suffer a witch to live." There is some debate about the translation of this line with many translations substituting the word "sorcerer" for witch. The etymology of sorcery is more specifically concerned with the conjuring of spirits than the more generic spell crafting of witchcraft. It follows then that the Bible can be interpreted to suggest that only the spirit conjuring element of magical practice is prohibited and the nature magic or non spirit orientated spell crafting practiced by witches can be accepted by Christians. There are several references to mediums and necromancers in the Bible which are stated to be "abominable practices" (Deuteronomy 18:9-14) and which support the idea that it is communicating with the departed that seems to be the element of witchcraft which is incompatible with Christianity.
Some Christian witches point to the actions of Jesus in support of the practice of magic in Christianity. For those not believing Jesus to be the Son of God it would be hard to deny him the title of witch in light of his magical achievements. If taken literally - turning water into wine, multiplying loaves and fishes hundreds of times over and walking on water are impressive feats for even the most advanced of witches. Even if the miracles are considered to be acts of hypnosis to instill belief in the crowds a credible case could still be made that manipulation on this scale is the practice of witchcraft.
Traditional witches may argue that the path of a true magical practitioner cannot be followed within the moral confines of Christianity as a core tenet of the Christian faith is to shun harming others. This is however not dissimilar to Wicca which has managed to incorporate the practice of magic with the moral imperative of "harm none" quite effectively. It could be argued that a witch who focuses his/her sole attention onto magic that causes no harm is limiting themselves as a witch but a practitioner of witchcraft is still a witch even if he/she chooses not to embrace all aspects of their craft.
Christian witches will often work closely with angels in the same way that a non Christian witch might invoke spirits or the elements. Christian witches may see angels as the protective embodiment of ancestors or they may choose to work with the traditional angels of Christian doctrine.
Prayer for some Christian witches is deemed a very similar process to that of magic in that the intent is articulated and actioned through the power of the mind but whereas in witchcraft the will of the witch is actualized directly, prayer is a petition for the intercession of deity. Whether prayer alone can constitute the definition of witchcraft depends on how the individual witch chooses to define the term "witchcraft". Generally to use the term "Christian Witch" in its most common application is to define an individual who uses a combination of both prayer and spell work in the united path of their craft and their religion.