Well, when a mommy and a daddy love each other very much, and then an Evil Wizard (or just a crazy one) swoops down and squishes them together with something rather bizarre, or goes old school and stitches parts of them together with parts of something else, you get half-thingsthatdon'tbreed.
Half-Illithid is a misnomer, as it refers to stuff that isn't capable of turning into a full illithid that gets a tadpole stuffed into it's cranium regardless.