It's a joke, of course: tan + anorexic.
And, well, anorexia is the ideal thing to make jokes about, isn't it. There's nothing like a long period of decline and misery leading towards the eventual death of a fellow human being to have us all rolling in the aisles.
Mental illness? Hilarious. And, I mean, a mental illness revealing itself as a disinclination to eat has so much in common with a desire to keep your tan topped up, hasn't it.
Oh dear. I try to enjoy language in all its forms, but I'm going to make an exception with this horrible word. After all, surely it's only ever used by complete morons.
And the last thing I like to think of myself as being is complete.
The Sun-bather by Henry Scott Tuke
Word Not To Use Ever Under Any Circumstances Whatsoever: tanorexic. Oddly enough, tan may ultimately have something to do with an Irish word that means thin. It's definitely connected to the Latin tannum, which means tanbark. Orexis is the Greek for appetite, so tanorexic is more or less okay from that point of view. But not from others.