Regarding the fact that this is still somehow a hot topiс in English language-speaking communities I need to stress out that is a serious and respectful question without even a trace of intention to mock someone's preferences or to doubt one's right to self-identification.
Quite often in twitter profile people point out personal pronoun they prefer. As a non-native speaker what I don't understand why one need to provide the pronoun in two cases. For instance, consider following profiles: "he / him" or "she / her". If one prefer to be referred "he" in Nominative case, doesn't it imply that in Dative/Accusative (or whatever is the right term in English) they will expect to be referred as "him" and for Genitive they will prefer "his".
So, the question is: why there it's usually common to list two forms and why exactly this two forms: not "he" / "his", for instance.