May be she is desperately lonely and is craving for real human connection. She might not be good at approaching personal relationships and thus coming off wrong by asking you about the one thing she knows about you. Of course, you have no obligation to talk to her about it. I usually tell people “that is my least fav subject to talk about”. And I use this sentence quite generously, almost about anything i don’t feel comfortable talking.
I am suggesting this because I too was judged as being “weird” (not gossipy) because I was getting too personal with people by asking questions. I was craving (and still do) close human connections and that was clouding my vision and hence my social behavior was making others question my intentions. My only intention, however, was to connect.