The history of it is that Napanii was invented to service the need for a lingua franca in the newly-formed State. It's a constructed language, in other words. The thing to remember about constructed languages is that they use consistent and rigid rules for things like pluralization and so on. In English we have oddities like "sheep/sheep", "mouse/mice" and "goose/geese" because the language was mashed together by common usage over centuries and has loaned both words and grammar from foreign dialects. If English were a constructed, consistent language then the plurals would me "Sheeps", "Mouses" and "Gooses"
"-haan" literally just means "citizen". It's a gender-neutral term by definition. The English equivalent to the feminine "haani" would be "citizeness" which is an absurd, divisive construct which serves only to suggest that men and women are different kinds of citizen. That's not in keeping with how I think of Caldari attitudes.
Remember, the whole "-haan" thing was inspired by the Japanese "-san" tradition, which itself is gender-neutral.
The correct pluralizations for all Napanii nouns and verbs is actually -t/-et/-at/-ut. So the plural term "citizens" would be "Haanat"
"-i" is the stem for infinitive expression and present action. Applying it to "haan" results in the term you use when referring to citizenry in an abstract or objectified way.
"I am a citizen" = "Nei haani
"This citizen" = "Hanta haani"
"Those citizens" = "Soyi haanat"
"We citizens" = "Kiriit haanat"
"All citizens of the Caldari State" = "Haanaten Caldarin Vaktikun"
So in fact, "haani" when used to refer to a woman treats her as an object rather than as a person. Which suggests a rather more sinister explanation than the cutesy "you're pregnant! I'm going to start calling you citizens-plural now."