One of a kind

Why does the phrase "one of a kind" mean the opposite of what it says? After all, if you're only one example of an entire kind, doesn't that mean the opposite of being unique?

Now, if you were "a kind of one", that would be a very stilted (in modern parlance) phrase that would mean the right thing, analogous to "in a class by yourself" in denotation.

I'm sure there's some perfectly innocuous (and probably depressingly dull) explanation for the phrase's apparent contradiction of meaning. What I find more interesting is that I have used the phrase for decades without even realizing the contradiction, and so does almost everyone else. We all learned the phrase as a semantic unit at a young enough age that we didn't take it apart and try to figure out how its pieces work. By time we were old enough to do that, even in the habit of doing it, it was already firmly established and we never thought to go back and reconsider it.

I remember the first time I thought about how the town Stony Brook, near where I was born and raised, meant "stony brook" and therefore was probably named for an actual stony brook (and I even guessed right which brook it was, once I realized that). I was, at the time, in college (at SUNY Stony Brook in fact) and had known the place name my whole life. Sometimes outsiders can see these kinds of things far far quicker.