Are you a doctor?

A person can be a doctor of many things.  Being a physician is only one of them.  The title "doctor" comes from old Christian monestaries and was conveyed when a scholar had seemed to reach exceptional levels of knowledge.

From the Wikipedia:

"Dr." redirects here. For other uses, see DR (disambiguation).

Doctor is an academic title that originates from the Latin word of the same spelling and meaning.[1] The word is originally an agentive noun of the Latin verb docēre [dɔˈkeːrɛ] 'to teach'. It has been used as an academic title in Europe since the 13th century, when the first doctorates were awarded at the University of Bologna and the University of Paris.

https://en.wikipedia.org/wiki/Doctor_(title)