grammar - How often do you go to "the" or "a" dentist?

I answered the below question and got it wrong. I wonder why? It was a fill in the blank type question.

How often do you go to ______ dentist?

I wrote "How often do you go to a dentist?" The correct answer is "How often do you go to the dentist?" I have never been to the same dentist in my life. I have only been to the dentist five times and each time is a different one.

Why is "a" wrong?