They are, and most of the time the ones mistreating half-elves are those with prior prejudice. A majority of the time the parents are alright, but some end up abandoning their children. Interbreeding can cause health problems in the child, but it's impossible to know whether to not that will happen. Sometimes the child will be more like a human, or more like an elf.

[He adjusts his glasses.]

To be honest, I'm not quite sure why there is so much hate for half-elves. Prejudice is probably the best explanation for it.