But she doesn't get teased because she writes about her relationships, it's because most relationships she's had have been with super high profile celebrities, and that generates interest in the subjects of her songs. She cites Ed Sheeran as someone who never has this problem with the media, but there were articles speculating if Don't was about Ellie Goulding. So I just can't see her "sexism" angle.
She also has these high profile relationships near/surrounding releases of her music. It's all too convenient. It seems to me she wants to have her cake and eat it too.