The word “jihad" means to “strive" or “struggle," and in the Muslim world it has traditionally been used in tandem with “fi sabilillah" (in the path of God). The term has long been taken to mean either a quest to find one"s faith or an external fight for justice. It makes sense, then, for terrorists to associate themselves with a term that has positive connotations. For the US to support them in that effort, however, is a fundamental strategic mistake.
First, to call a terrorist a “jihadist" or “jihadi" effectively puts any campaign against terrorism into the framework of an existential battle between the West and Islam. Second, these words locate the ideological battle exactly where the extremists want it to be.
Third, when American leaders use this language it sends a confusing message to the Muslim world, showing ignorance on basic issues and possibly even raising doubts about American motives.