I'm not sure why it offends me. I think because of the term "Half-caste" which was (and still is by racists) used to describe aboriginal people who had some white parentage in the colonial days. If you read the second paragraph here it specifically mentions the use in Australia. Something about having to describe anything non-white about them as being 'half', I really don't know it just seems derogatory to me. They are a whole person, not white and half something else. They are the two races together one is not superior.
For what its worth I was always offended growing up when people referred to my brothers (who have a different mother) as my half-brothers. Though that is a totally different thing ...But they weren't half anything, they were completely fully my real brothers.
Waiting2bemommy- If my child as an adult decides they are comfortable describing themselves that way it is absolutely fine with me. However me assigning that term to them now, which I feel is in some way derogatory is a very different thing, especially as I am white myself. If I was also mixed race and decided to call my kids that then I would be coming from a place of understanding.
Oka-San + CappucinosMom- The line "his father is (insert race)" doesn't work for us as my children were conceived by a donor. And we don't refer to our donor as 'father'. And I don't particularly want to get into conversations about how my children were conceived with strangers at the park, kwim? Its hard enough to dodge it as it is with the kinds of questions strangers always ask me, without being blatant about it.
La Mamita- I consider myself American and Australian as my mom is American and dad Australian, so that makes 3 nationalities to add together and explain and it becomes a bit of a mouthful. I could just say Caucasian instead I guess, but sounds a bit formal for the kinds of discussions/people where it comes up. But still better than saying half