Identical Cousins. Wait, what?

I don't know how it never registered when I was a kid, but what the hell was up with the premise of the Patty Duke Show?

"They're cousins, identical cousins and you'll find... they laugh alike, they walk alike, some times they even talk alike.... you could lose your mind! when cousins! are two of a kind!"

I mean, seriously: how did it never occur to me that there's no such thing as "identical cousins"? Also, why do I still know the theme song to a show that was already in reruns before my mother had even graduated high school? Hrm... I just looked it up on wikipedia and evidently I don't remember all of the theme song. Here are the lyrics in full (just try to wrap your head around all the ways in which none of this makes sense):

Meet Cathy, who's lived most everywhere,
From Zanzibar to Barclay Square.
But Patty's only seen the sights
A girl can see from Brooklyn Heights - what a crazy pair!

But they're cousins,
Identical cousins all the way.
One pair of matching bookends,
Different as night and day.

Where Cathy adores a minuet,
The Ballet Russes, and crepe suzette,
Our Patty loves to rock and roll,
A hot dog makes her lose control - what a wild duet!

Still, they're cousins,
Identical cousins and you'll find,
They laugh alike, they walk alike,
At times they even talk alike -
You can lose your mind,
When cousins are two of a kind!

Okay, I'll admit it, that was mostly filler. I don't really have anything more to say about this other than to invite you to really fully consider the insanity that is the idea of IDENTICAL COUSINS.

Also, is the bit about the hot dog innuendo? If so: gross.