User blog comment:Gundam Legilis/Welcome To Beacon In Depth - The characters/@comment-190.142.159.10-20140802024225/@comment-96.254.157.84-20140802024701

I firmly believe that Ozpin already knows Blake was a White Fang and was giving her a chance to tell him, though she decided not to in the end. Then when he asks "who are you?" I think he was asking where her loyalties lie (Beacon or the White Fang).