In my German grammar book, there's the following table:
Can somebody explain me why it's vom? Is it because Arzt is a profession or is it because it's a masculine subject?
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It becomes apparent when you take a look at the first row Orte. There the article isn't contracted (although colloquial it becomes aus dem -> ausm).
For people you always use von if it answers the questions "Woher?". The special case is not with Arzt but rather with Eigennamen such as Jana. Normally, you would also need an article there (and in some dialects, an article is put in front of a name), i.e.
Ich komme von dem Arzt (short: vom)
Ich komme von der Pflege (colloquial: vonner)
Ich komma von dem Denkmal (short: vom)
Ich komme von der Jana (Hessian dialect)
Ich komme von dem Tim (Hessian dialect)
Ich komme von Ärzten (indefinite plural, no article needed)
Ich komme von den Ärzten (definite plural)
In addition I'd like to mention that one says 'ich komme vom Arzt' even if the doctor is female. To be more accurate, you'd rather say 'ich war bei meiner Ärztin' than 'ich war bei der Ärztin' because 'bei der Ärztin' would imply that the person talked to knows who the (female) doctor is.
The reason is that der in 'der Arzt' is a generalizing article meaning any person (even more than one) that gives medical treatment to the speaker. So normally you would neither say 'ich komme von Ärzten' nor 'ich komme von den Ärzten', but 'ich komme vom Arzt' even if you had dealings with more than one doctor. 'Ich war bei drei Ärzten' means, that you have had three different treatments at three different dates.
Similarly, you would say 'ich war beim Biobäcker und habe dein Körnerbrot gekauft' even if there was no baker and no man at all but just a young lady selling baked goods. And you would say 'ich war bei drei Bäckern / in drei Bäckereien, um diese verdammten Körnerbrötchen zu bekommen.'