Prentiss asks Hotch to debrief her on the plane. She should have asked to be briefed. A debriefing happens afterwards.
The Nietzsche quote from this and the pilot, is an abbreviation of the original. Interestingly, in Extreme Aggressor (2005), the full quote is properly stated, "He who fights with monsters should look to it that he himself does not become a monster. And if you gaze long into an abyss, the abyss also gazes into you".