Why does it say 자기 means honey (im guessing its just a term of endearment) but then marks "Honey, introduce yourself" as wrong?
"Honey, introduce yourself" would be 자기, 자기 소개를 해. That's because 자기 also means "self".
If it was someone calling out to their boyfriend/girlfriend/wife/husband, they would have to say 자기야. If I called your name, 조나스야. My name, 다니엘아. Then continue the sentence.
So, when I first ran across this I thought the same thing. I looked into it and what I gathered was that the term 자기 when used as like a pet name for couples pulls from the definition of 자기 meaning "self". Basically when you use it, you're equating your significant other with yourself; they're your other half or soulmate.