@mahtan Not exactly, I think it's a word for any mixed blood. Probably more common to be a human/demon or maybe even human/angel than angel/demon (I feel like this story previously said the only reason Rin can survive at all is because her being part human acts like a buffer between the other two, which are just not able to mix ordinarily).
As for why he should just stop using it... Nobody even called Rin one until they all got here, and when someone did say it in front of her, they almost killed him for it afterward. Clearly the word is not just used to classify a group of people in an unbiased manner. To pull a stray Harry Potter reference out of nowhere so I don't have to reference actually offensive terms from the real world, perhaps it's more like saying "mudblood" than "muggle born."