“he moved David against them.” This is the Semitic idiom of permission. An idiom is “a phrase or expression whose meaning cannot be understood from the ordinary meanings of the words in it.” E. W. Bullinger summarizes it well in his book, Figures Of Speech Used In The Bible; under the entry “Idioma,” number 4: “active verbs were used...to express not the doing of the thing, but the permission of the thing which the agent is said to do.” The idiom of permission is the reason why many verses in the Bible seem to attribute evil actions to God.
It is widely recognized by scholars that in Semitic languages the active verb can be used in a permissive sense. For example, in The Emphasized Bible by Joseph B. Rotherham, the phrase often translated as, “I will harden his [Pharaoh’s] heart” is translated as “I will let his heart wax bold” (cp. Rotherham, Exod. 4:21). Rotherham translates 2 Samuel 24:1 as: “…so that he suffered [allowed] David to be moved against them.” In other words, God was so angry against Israel that he could not protect them the way He would have liked and thus allowed Satan to work through David to cause disaster in Israel (cp. 1 Chron. 21:1, which shows that it was actually Satan who moved David to count Israel). For more on the idiom of permission, see commentary on Romans 9:18].