He is an entrepreneur should not be wrong, "he is a entrepreneur" is what I was given as the proper answer, that is not right in English grammar.
Entrepreneur and businessman are different words and can have different meanings. Entrepreneur is better translated to empreendedor.
There is not "um" in the sentence! So why is it translated to "a" in English?
a rule involving occupations Portguese vs English.
In Romance languages, occupations function as adjectives when used this way.