That's YOUR fault for listening to Cher in the first place!
Additionally, the notion that "half-breed" is deragotory term fails on two counts:
A) It assumes intent on the part of the speaker (ie me) and
B) Unless the speaker is of neither of the referenced races, it would self-insulting. I, being white, have plenty of other direct insults to apply to my own race without resorting to some watered down subterfugal mockery.
Besides, renouncing a term like half-breed places humans above animals, which I don't. Anybody got that Carlin clip handy where he talks about honest use of language versus euphamism? Basically that's what this is.