Or at least that's true in the same sense that there's "no such thing as a fish". Which is to say that, obviously, antelopes exist but they aren't a scientifically definable group of animals. Or that, if they were, that group wouldn't map closely to what the regular English word "antelope" is supposed to mean.
The word entered English during the Rennaissance, and descends, via Latin, from the Greek "ανθολοψ". That first appears in the 4th century (so not old enough to be Ancient Greek, as such) and referred at the time to a mythical beast said to live along the Euphrates that had horns so sharp and serrated that it used them to cut down trees. We don't know why the Byzantine Greeks called it this, but there's not some "lope" that it's "ante" to (nor, to use most other European languages, is it an anti-lope); it's just a coincidence that the word sounds that way. For all we know, they were borrowing a word from some other, older language spoken somewhere out east.