I'm also sincerely interested in why the "What are you?" question is felt to be so offensive ... aside from a situation where the person asking seems to have nefarious intentions, like: to know if you're of a certain ethnicity they'd rather avoid, or for them to know what racist things they can/cannot say in front of you. Or maybe some think it's "too personal". But idk, I mean "What do you do for a living?" doesn't seem to get people hot, usually. And I consider that somewhat personal too (not that I mind being asked).
There probably are reasons for feeling offended that I just haven't considered, as I'm just one person with one set of experiences. Personally, I just figure there's nothing wrong with someone expressing some curiosity about me, and in a way, it's flattering because there's something they find interesting about me. Plus I figure they have the right to ask me whatever they want and I have the right to answer, or not.