[christudor]

Because doctor comes from the passive doctus ('having been taught', i.e. learned) rather than the active docens ('teaching, instructing').

[lou1306]

Not really. Doctor means "teacher" in classical Latin.

[FabHK]

Good point. English has both actor (=someone who acts) and agent (=someone who acts) from agere = to act, and both doctor (=someone who teaches) and docent (=someone who teaches) from docere = to teach.