Ok, question. I hope you don't mind me asking, but I see American's using the phrase 'Could care less', over here we use the phrase 'Couldn't care less', are you meaning the same thing?
Unfortunately, yes. It has somehow become common here to say "could care less" when one means that they "COULDN'T care less." It really is just common sense. If people would stop to think about how it sounds and break it apart, they would realize that what they're saying doesn't make any sense whatsoever. To say that you "COULD care less" implies that you DO care, but to say that you "COULDN'T care less" says that you really don't give a damn.
Where you see most of this argument is in professional journals where they have strict rules on language.
English is such a fluid language, however journals are usually slow to accept and step away from the Oxford English Dictionary.
I think it's unlikely that the OED lists Euthanatize. It would likely be spelled Euthanatise if it were used in British English.
Euthanatize seems pointlessly pedantic to me. There was not a verb form of euthanasia until America started progressively turning all nouns into verbs in the second half of the 20th century. To then complain that a recently invented word does not correctly follow its Greek roots just seems like arguing over whether a professional chef would serve Twinkies at room temperature or refrigerator temperature.