A set is countably infinite if and only if there is a one-to-one mapping from the positive integers to the set in question. That's a definition. It's no more a "contradiction in terms" than any of the hundreds and hundreds of other definitions in math.
This is where English fails as the language of mathematics. “Countably infinite” IS a contradiction in the common sense of the terms. But they have a special meaning in math that allows the apparent violation of semantic logic.