This is simply the British spelling of homeopath. A homeopath is a person who treats illness with homeopathy: a hugely watered-down dose of something that would, in a large amount, cause the same sort of trouble the patient already has. The working idea is "like treats like." You say it HOME-ee-oh-path; the extra e in the middle is not a second vowel you have to pronounce. British English kept oe in a handful of medical words that came through German or older Latin (homoeopath, diarrhoea, oestrogen); American English shortened them (homeopath, diarrhea, estrogen). In a Taiwan classroom the American spelling is the one you will almost always see, so homoeopath can look like a typo. It is not. Same job, same person, different national spelling. Though actually, even in Britain the oe form is fading, and many UK sites now write homeopath. Whether the treatment works is a much louder argument than the spelling.