"My girlfriend is a student."
Translation:Моя дівчина студентка.
In another sentence: "She's works as a secretary", we had to use "секретар" instead of "секретарка", and in the discussion is was explained that you used the masculine for professions (and, in addition, "секретарка" had sexual connotations...) So, would "студент" be possible here, in addition to "студентка"?
The thing with feminine for professions it's just that some are more usual and common than others. There's no "rule". Words like директорка, програмістка, режисерка or юристка are less common, for some professions there are no feminine nouns at all: there's no водійка (from водій) and капітанша and генеральша are colloquial words for captain's and general's wives and not for girls in that position. Than there are professions for which both masculine and feminine nouns are equally common (for girls): вчитель and вчителька, журналіст and журналістка (although people tend to have their preferences over one of the words). And finally there are professions where it would be rather weird to use masculine: телеведуча (TV presenter), акторка, поетеса or поетка (poet). Student is one these last ones
Basically, what we can see from it is that all of those jobs were traditionally occupied by men, so feminine nouns are still trying to make it to the standard language. A lot of feminine nouns are seen as colloquial and thus they are not that widely used