It seems annoying because personal names like Jenny and John have grammatical gender in English, so the unknown grammar use of they/them/their seems unnatural.

It seems annoying because personal names like Jenny and John have grammatical gender in English, so the unknown grammar use of they/them/their seems unnatural. It's also perhaps why similar-sounding names are generally spelt differently between genders, e.g. Danny/Danni, Jerry/Jeri, Tony/Toni, Billy/Billie, Francis/Frances, Robin/Robyn, Sidney/Sydney.