I was reading a past post that involved the sentence:

"I am his/her/your aunt."

My question is, why do we have to specify "your" aunt if, in context, it's obvious you (the aunt) couldn't be anyone else's aunt? "I am aunt" conveys the same meaning, but is obviously grammatically incorrect.

Many other languages don't do this when the person whose aunt she is is clear already:

Japanese: (the aunt is known to be related to the person whose aunt she is) "Kono hito no namae wa Tomoko desu. Oba-san desu." Lit.=> "This person's name equals Tomoko. (She) equals aunt."

Utilitarian, if nothing else... Emotion: smile)) But also consistent with Japanese grammar.

In that case I guess "I am the aunt" would be okay? Sounds like adding "the" in English just implies that there can only be ONE aunt, which isn't want I want to say. So why do we need a word (his/her/your) there at all?
Because all singular countable nouns which are not implicitly determined, need to be explicitly determined. In general, the simplest way to do this is with the articles "a" and "the". In English, however, the possessives implicity provide determination, so an article is not necessary if you use "his", "her", etc.

"I am aunt" may not be grammatically correct, but "I am Aunt" is. Just capitalize it - bingo - one proper noun. And all proper nouns are implicity definite.

Incidently, contrary to popular belief, "the" does not imply uniqueness, only known-ness. It is perfectly okay to say "The chair is squeaking again" in a room containing five chairs, providing it's obvious which chair you're talking about. (Maybe only one of them ever squeaks).