Obsession with talking to oneself in the mirror. what illness causes this?

Might be fine!: That you call it an obsession might suggest ocd - do you feel significant anxiety if you are prevented from doing it? If not, don't call it obsessive. Talking about things that trouble you (even to yourself) can actually be helpful for finding strategies. Testing things out before taking action. Try not to see illness where there might be none. Best!

Perhaps none: This discussion you are having with self is at best summarized by the conditions under which it occurs. For instance, many elite athletes, motivationalist, spiritualists, etc, all do the same. Of course, with purpose in mind --achieving and/or performing at a higher level. If your mirrored engagement is increasingly self-critical, and destructive, then maybe its time to seek professional help.