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Hmmm... It is really very quirky. Sometimes Nominative is also possible and even preferable for был and будет. Let's see... Genitive is used to describe the property, while Nominative - to describe...

Yes, this is a quirk. The verb "быть" (был-есть-будет) requires instrumental for its direct object in all forms but Present tence.

Быть врачом.
Он был врачом.
Он (есть) врач.
Он будет врачом.
...