A few of the many reasons that Bach scholars question its authorship is 1) Bach would not have ended the piece with a minor plagal cadence (take a peek at his Little Fugue in G Minor as an example of how he would have ended it). 2) Bach would not have started the piece in octaves. 3) The original manuscript was written in D minor but without a flat. 4) It is not in the intellectual style of Bach. Certainly the piece was written to dazzle and show off but it does not have the contrapuntal sophistication of Bach and, the fugue is not at all complicated or brilliantly worked out as much of Bach's other fugues are. 5) The diminished seventh is used throughout the piece repetitiously and rather naively.
The original manuscript was in the handwriting of Johann Rinck (Johannes Ringk) who was a student of Johann Peter Kellner. Kellner knew Bach and was a student of Johann Christian Kittel and Kittel was Bach's last student. Many music scholars beleive that the piece was actually a composition of Kellner's which Rinck copied since it is in Kellner's style.
The greater question is: Does anyone care? Not in the least. It is still a great piece of music hitting the bulls-eye for generations of listeners.