I'm not usually offended it just gets annoying to explain that both my parents&grandparents are black.I don't like to get into how my great great grandparents+ were biracial or whatever,because I don't really count that.
If the person that asks me is mixed/bircial then I can understand that they see someone they can relate to.But what I don't like it a total stranger asking me what/who I am its just not a great opener.