The word for a phrase that contradicts itself is a phrase that contradicts itself.
Oxymoron is Greek. Etymonline gives it as the neuter of oxymōros, "pointedly foolish," which joins oxys, "sharp," with mōros, "stupid." Merriam-Webster describes the Greek as "sharp, keen" plus "foolish." Sharp and foolish do not belong together, so the name does exactly what it says.
English first recorded the word in the 1650s as a technical term in rhetoric. Merriam-Webster gives 1656. It named a figure of speech that joins apparently contradictory words for emphasis. Its standard example is "cruel kindness." Merriam-Webster also lists "bittersweet" among the words it has in mind.
Many people assume that the "moron" in oxymoron is the English word moron. They share a source, but the connection is only that. Merriam-Webster puts it plainly: the two words "have little in common except that both words come from the Greek word for foolish." Etymonline likewise names the Greek mōros as the source of English moron.
The modern meaning has loosened. Etymonline notes that the word is now often used for any "contradiction in terms." That is a looser idea than the original figure, which was a deliberate device, a sharp point made through apparent nonsense.
Merriam-Webster's examples show the range. William Safire used "bleeding-heart conservative" in 1990. Paul Fussell called "precision bombing" a comical oxymoron in 1989. A 1996 Rolling Stone piece described "Broadway rock musical" as one.
One question the dictionaries do not settle is whether a person can be an oxymoron. Merriam-Webster says usually not, since the term refers to contradictory words, not contradictory people.
So the word came into English as a precise rhetorical label and drifted into a label for any contradiction in terms. The origin is the part that holds up: Greek for "sharp fool," two opposites in one word.